Question 1

Find the standard-form equation of the hyperbola whose graph is shown.
-

Accepted Answer

A)  $\frac{(\mathrm{x}-2)^{2}}{16}-\frac{(\mathrm{y}+4)^{2}}{9}=1$ 
B)  $\frac{(x+2)^{2}}{16}-\frac{(y-4)^{2}}{9}=1$ 
C)  $\frac{(x+2)^{2}}{9}-\frac{(y-4)^{2}}{16}=1$ 
D)  $\frac{(\mathrm{x}-2)^{2}}{9}-\frac{(\mathrm{y}+4)^{2}}{16}=1$ 
A)  $\frac{(\mathrm{x}-2)^{2}}{16}-\frac{(\mathrm{y}+4)^{2}}{9}=1$ 
B)  $\frac{(x+2)^{2}}{16}-\frac{(y-4)^{2}}{9}=1$ 
C)  $\frac{(x+2)^{2}}{9}-\frac{(y-4)^{2}}{16}=1$ 
D)  $\frac{(\mathrm{x}-2)^{2}}{9}-\frac{(\mathrm{y}+4)^{2}}{16}=1$

Question 2

Solve the system by the substitution method.
-$5 x^{2}-2 y^{2}=-12$
$4 \mathrm{x}^{2}+5 \mathrm{y}^{2}=96$

Accepted Answer

A)  $(2,-4),(2,4)$ 
B)  $(2,4),(4,2),(-2,-4),(-4,-2)$ 
C)  $(-2,-4),(-4,-2)$ 
D)  $(2,4),(-2,4),(2,-4),(-2,-4)$ 
A)  $(2,-4),(2,4)$ 
B)  $(2,4),(4,2),(-2,-4),(-4,-2)$ 
C)  $(-2,-4),(-4,-2)$ 
D)  $(2,4),(-2,4),(2,-4),(-2,-4)$

Question 3

Graph the parabola. State the vertex of the parabola.
-$y=-x^{2}-2 x-8$

Accepted Answer

A)  vertex $ (-1,7) $
  
B)  vertex $ (-1,-7) $
  
C)  vertex $ (1,7) $
  
D)  vertex $ (-1,-9) $
  
A)  vertex $ (-1,7) $
  
B)  vertex $ (-1,-7) $
  
C)  vertex $ (1,7) $
  
D)  vertex $ (-1,-9) $

Question 4

Solve.
-The planets in a certain solar system have a path that is an ellipse, with Star A as one of the foci. Planet $X$ has a perihelion of 588.6 million miles and an aphelion of 631.8 miles. Find an equation for Planet X's orbit. Express your answer with $a$ and $b$ in millions of miles, rounded to the nearest tenth of a million.

Accepted Answer

A)  $\frac{x^{2}}{610.2^{2}}+\frac{y^{2}}{609.8^{2}}=1$ 
B)  $\frac{x^{2}}{609.2^{2}}+\frac{y^{2}}{610.8^{2}}=1$ 
C)  $\frac{x^{2}}{610.8^{2}}+\frac{y^{2}}{609.2^{2}}=1$ 
D)  $\frac{\mathrm{x}^{2}}{609.8^{2}}+\frac{\mathrm{y}^{2}}{610.2^{2}}=1$ 
A)  $\frac{x^{2}}{610.2^{2}}+\frac{y^{2}}{609.8^{2}}=1$ 
B)  $\frac{x^{2}}{609.2^{2}}+\frac{y^{2}}{610.8^{2}}=1$ 
C)  $\frac{x^{2}}{610.8^{2}}+\frac{y^{2}}{609.2^{2}}=1$ 
D)  $\frac{\mathrm{x}^{2}}{609.8^{2}}+\frac{\mathrm{y}^{2}}{610.2^{2}}=1$

Question 5

Solve the system by the substitution method.
-$x^{2}+y^{2}=4$
$\mathrm{x}^{2}-\mathrm{y}^{2}=4$

Accepted Answer

A)  $(2,0),(-2,0)$ 
B)  $(2,0),(2,2)$ 
C)  $(2,2),(-2,2)$ 
D)  No solution 
A)  $(2,0),(-2,0)$ 
B)  $(2,0),(2,2)$ 
C)  $(2,2),(-2,2)$ 
D)  No solution

Question 6

Find the distance between the pair of points. Round to the nearest tenth if necessary.
-$(47,2)$ and $(26,44)$

Accepted Answer

A)  7445 
B)  $\sqrt{7445} \approx 86.3$ 
C)  $21 \sqrt{5} \approx 47$ 
D)  3213 
A)  7445 
B)  $\sqrt{7445} \approx 86.3$ 
C)  $21 \sqrt{5} \approx 47$ 
D)  3213

Question 7

Find the equation of the parabola of the form $x=a y^{2}+b y+c$ that passes through the given three points.
-$(49,-1),(37,3),(93,10)$

Accepted Answer

A)  $x=y^{2}-5 y+43$ 
B)  $x=y^{2}-9 y+20$ 
C)  $x=3 y^{2}-y+74$ 
D)  $x=2 y^{2}-y+64$ 
A)  $x=y^{2}-5 y+43$ 
B)  $x=y^{2}-9 y+20$ 
C)  $x=3 y^{2}-y+74$ 
D)  $x=2 y^{2}-y+64$

Question 8

Graph the parabola. State the vertex of the parabola.
-$ y=(x+4)^{2}+3 $

Accepted Answer

A)  vertex $ (-3,4) $
  
B)  vertex $ (3,-4) $
  
C)  vertex $ (-4,3) $
  
D)  vertex $ (4,3) $
  
A)  vertex $ (-3,4) $
  
B)  vertex $ (3,-4) $
  
C)  vertex $ (-4,3) $
  
D)  vertex $ (4,3) $

Question 9

Find the midpoint of the line segment that connects the given points.
-$(-6,-1)$ and $(7,8)$

Accepted Answer

A)  $\left(\frac{1}{2}, \frac{7}{2}\right)$ 
B)  $(-13,-9)$ 
C)  $(1,7)$ 
D)  $\left(-\frac{13}{2},-\frac{9}{2}\right)$ 
A)  $\left(\frac{1}{2}, \frac{7}{2}\right)$ 
B)  $(-13,-9)$ 
C)  $(1,7)$ 
D)  $\left(-\frac{13}{2},-\frac{9}{2}\right)$

Question 10

Solve the problem.
-Arches in the shapes of parabolas are often used in construction. Find the equation of a parabolic arc that is 20 feet high at its highest point and 28 feet wide at the base, as illustrated in the figure. Place the origin at the midpoint of the base.

Accepted Answer

A)  $y=-x^{2}+28$ 
B)  $y=\frac{5}{49} x^{2}+20$ 
C)  $y=-x^{2}+20$ 
D)  $y=-\frac{5}{49} x^{2}+20$ 
A)  $y=-x^{2}+28$ 
B)  $y=\frac{5}{49} x^{2}+20$ 
C)  $y=-x^{2}+20$ 
D)  $y=-\frac{5}{49} x^{2}+20$

Question 11

Solve the system by the substitution method.
-$5 x^{2}-y^{2}=10$
$\mathrm{y}=\mathrm{x}^{2}-2$

Accepted Answer

A)  $(-\sqrt{2}, 0),(\sqrt{2}, 0)$ 
B)  $(-\sqrt{7}, 5),(\sqrt{7}, 5)$ 
C)  $(0,-\sqrt{2}),(0, \sqrt{2}),(5,-\sqrt{7}),(5, \sqrt{7})$ 
D)  $(-\sqrt{2}, 0),(\sqrt{2}, 0),(-\sqrt{7}, 5),(\sqrt{7}, 5)$ 
A)  $(-\sqrt{2}, 0),(\sqrt{2}, 0)$ 
B)  $(-\sqrt{7}, 5),(\sqrt{7}, 5)$ 
C)  $(0,-\sqrt{2}),(0, \sqrt{2}),(5,-\sqrt{7}),(5, \sqrt{7})$ 
D)  $(-\sqrt{2}, 0),(\sqrt{2}, 0),(-\sqrt{7}, 5),(\sqrt{7}, 5)$

Question 12

Find the standard-form equation of the ellipse.
-

Accepted Answer

A)  $\frac{(\mathrm{x}+2)^{2}}{9}+\frac{(\mathrm{y}+5)^{2}}{16}=1$ 
B)  $\frac{(\mathrm{x}+2)^{2}}{16}+\frac{(\mathrm{y}+5)^{2}}{9}=1$ 
C)  $\frac{(\mathrm{x}-2)^{2}}{9}+\frac{(\mathrm{y}-5)^{2}}{16}=1$ 
D)  $\frac{(\mathrm{x}-2)^{2}}{16}+\frac{(\mathrm{y}-5)^{2}}{9}=1$ 
A)  $\frac{(\mathrm{x}+2)^{2}}{9}+\frac{(\mathrm{y}+5)^{2}}{16}=1$ 
B)  $\frac{(\mathrm{x}+2)^{2}}{16}+\frac{(\mathrm{y}+5)^{2}}{9}=1$ 
C)  $\frac{(\mathrm{x}-2)^{2}}{9}+\frac{(\mathrm{y}-5)^{2}}{16}=1$ 
D)  $\frac{(\mathrm{x}-2)^{2}}{16}+\frac{(\mathrm{y}-5)^{2}}{9}=1$

Question 13

Graph the circle. State the center and radius of the circle
-$(x+3)^{2}+(y-6)^{2}=4$

Accepted Answer

A)  center $(-3,6) ; r=2$
  
B)  center $(3,-6) ; r=2$
  
C)  center $(3,6) ; r=2$
  
D)  center $(-3,-6) ; r=2$
  
A)  center $(-3,6) ; r=2$
  
B)  center $(3,-6) ; r=2$
  
C)  center $(3,6) ; r=2$
  
D)  center $(-3,-6) ; r=2$

Question 14

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$.
-$\frac{x^{2}}{64}-\frac{y^{2}}{9}=1$

Accepted Answer

A)  center $ (0,0), a=8, b=3 $
  
B)  center $ (0,0), a=3, b=8 $
  
C)  center $ (0,0), a=3, b=8 $
  
D)  center $ (0,0), a=8, b=3 $
  
A)  center $ (0,0), a=8, b=3 $
  
B)  center $ (0,0), a=3, b=8 $
  
C)  center $ (0,0), a=3, b=8 $
  
D)  center $ (0,0), a=8, b=3 $

Question 15

Solve.
-An elliptical bicycle path is constructed in a local park. The equation of the ellipse that represents the path, in yards, is given by $\frac{\mathrm{x}^{2}}{1225}+\frac{\mathrm{y}^{2}}{4225}=1$. What are the length and the width of the bicycle path?

Accepted Answer

A)  length: $70 \mathrm{yd}$; width: $130 \mathrm{yd}$ 
B)  length: $130 \mathrm{yd}$; width: $70 \mathrm{yd}$ 
C)  length: $35 \mathrm{yd}$; width: $65 \mathrm{yd}$ 
D)  length: $65 \mathrm{yd}$; width: $35 \mathrm{yd}$ 
A)  length: $70 \mathrm{yd}$; width: $130 \mathrm{yd}$ 
B)  length: $130 \mathrm{yd}$; width: $70 \mathrm{yd}$ 
C)  length: $35 \mathrm{yd}$; width: $65 \mathrm{yd}$ 
D)  length: $65 \mathrm{yd}$; width: $35 \mathrm{yd}$

Question 16

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$.
-$25 x^{2}+36 y^{2}=900$

Accepted Answer

A)  center $ (0,0), a=5, b=6 $
  
B)  center $ (0,0), a=6, b=5 $
  
C)  center $ (0,0), a=5, b=6 $
  
D)  center $ (0,0), a=6, b=5 $
  
A)  center $ (0,0), a=5, b=6 $
  
B)  center $ (0,0), a=6, b=5 $
  
C)  center $ (0,0), a=5, b=6 $
  
D)  center $ (0,0), a=6, b=5 $

Question 17

Find the distance between the pair of points. Round to the nearest tenth if necessary.
-$(-3,1)$ and $(3,-7)$

Accepted Answer

A)  14 
B)  100 
C)  10 
D)  $\sqrt{14} \approx 3.742$ 
A)  14 
B)  100 
C)  10 
D)  $\sqrt{14} \approx 3.742$

Question 18

Find the standard-form equation of the hyperbola whose graph is shown.
-

Accepted Answer

A)  $\frac{x^{2}}{16}-\frac{y^{2}}{25}=1$ 
B)  $4 x^{2}-5 y^{2}=1$ 
C)  $\frac{x^{2}}{4}-\frac{y^{2}}{5}=1$ 
D)  $16 x^{2}-25 y^{2}=1$ 
A)  $\frac{x^{2}}{16}-\frac{y^{2}}{25}=1$ 
B)  $4 x^{2}-5 y^{2}=1$ 
C)  $\frac{x^{2}}{4}-\frac{y^{2}}{5}=1$ 
D)  $16 x^{2}-25 y^{2}=1$

Question 19

Find the center and radius of the circle by completing the square.
-$x^{2}+y^{2}-2 x-10 y+10=0$

Accepted Answer

A)  $(-5,-1) ; r=16$ 
B)  $(5,1) ; r=4$ 
C)  $(-1,-5) ; r=16$ 
D)  $(1,5) ; r=4$ 
A)  $(-5,-1) ; r=16$ 
B)  $(5,1) ; r=4$ 
C)  $(-1,-5) ; r=16$ 
D)  $(1,5) ; r=4$

Question 20

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$.
-$3 x^{2}+7 y^{2}-63=0$

Accepted Answer

A)  center $ (0,0), a=\sqrt{7}, b=\sqrt{3} $
  
B)  center $ (0,0), \mathrm{a}=3, \mathrm{~b}=\sqrt{21} $
  
C)  center $ (0,0), a=\sqrt{21}, b=3 $
  
D)  center $ (0,0), \mathrm{a}=\sqrt{3}, \mathrm{~b}=\sqrt{7} $
  
A)  center $ (0,0), a=\sqrt{7}, b=\sqrt{3} $
  
B)  center $ (0,0), \mathrm{a}=3, \mathrm{~b}=\sqrt{21} $
  
C)  center $ (0,0), a=\sqrt{21}, b=3 $
  
D)  center $ (0,0), \mathrm{a}=\sqrt{3}, \mathrm{~b}=\sqrt{7} $

Find the standard-form equation of the hyperbola whose graph is shown. -

Solve the system by the substitution method. - $5 x^{2}-2 y^{2}=-12$ $4 \mathrm{x}^{2}+5 \mathrm{y}^{2}=96$

Graph the parabola. State the vertex of the parabola. - $y=-x^{2}-2 x-8$ $Graph the parabola. State the vertex of the parabola. - y=-x^{2}-2 x-8$

Solve the system by the substitution method. - $x^{2}+y^{2}=4$ $\mathrm{x}^{2}-\mathrm{y}^{2}=4$

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $(47,2)$ and $(26,44)$

Find the equation of the parabola of the form $x=a y^{2}+b y+c$ that passes through the given three points. - $(49,-1),(37,3),(93,10)$

Graph the parabola. State the vertex of the parabola. - $y=(x+4)^{2}+3$ $Graph the parabola. State the vertex of the parabola. - y=(x+4)^{2}+3$

Find the midpoint of the line segment that connects the given points. - $(-6,-1)$ and $(7,8)$

Solve the problem. -Arches in the shapes of parabolas are often used in construction. Find the equation of a parabolic arc that is 20 feet high at its highest point and 28 feet wide at the base, as illustrated in the figure. Place the origin at the midpoint of the base.

Solve the system by the substitution method. - $5 x^{2}-y^{2}=10$ $\mathrm{y}=\mathrm{x}^{2}-2$

Find the standard-form equation of the ellipse. -

Graph the circle. State the center and radius of the circle - $(x+3)^{2}+(y-6)^{2}=4$ $Graph the circle. State the center and radius of the circle - (x+3)^{2}+(y-6)^{2}=4$

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$ . - $\frac{x^{2}}{64}-\frac{y^{2}}{9}=1$ $Graph the hyperbola. Give the coordinates of the center as well as the values of a and b . - \frac{x^{2}}{64}-\frac{y^{2}}{9}=1$

Solve. -An elliptical bicycle path is constructed in a local park. The equation of the ellipse that represents the path, in yards, is given by $\frac{\mathrm{x}^{2}}{1225}+\frac{\mathrm{y}^{2}}{4225}=1$ . What are the length and the width of the bicycle path?

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$ . - $25 x^{2}+36 y^{2}=900$ $Graph the ellipse. Give the coordinates of the center, as well as the values of a and b . - 25 x^{2}+36 y^{2}=900$

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $(-3,1)$ and $(3,-7)$

Find the standard-form equation of the hyperbola whose graph is shown. -

Find the center and radius of the circle by completing the square. - $x^{2}+y^{2}-2 x-10 y+10=0$

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$ . - $3 x^{2}+7 y^{2}-63=0$ $Graph the ellipse. Give the coordinates of the center, as well as the values of a and b . - 3 x^{2}+7 y^{2}-63=0$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Sequences, Series, and the Binomial Theorem

Filters

Exam 10: Conic Sections

Find the standard-form equation of the hyperbola whose graph is shown. -

Solve the system by the substitution method. - 5x2−2y2=−125 x^{2}-2 y^{2}=-125x2−2y2=−12 4x2+5y2=964 \mathrm{x}^{2}+5 \mathrm{y}^{2}=964x2+5y2=96

Graph the parabola. State the vertex of the parabola. - y=−x2−2x−8y=-x^{2}-2 x-8y=−x2−2x−8

Solve the system by the substitution method. - x2+y2=4x^{2}+y^{2}=4x2+y2=4 x2−y2=4\mathrm{x}^{2}-\mathrm{y}^{2}=4x2−y2=4

Find the distance between the pair of points. Round to the nearest tenth if necessary. - (47,2)(47,2)(47,2) and (26,44)(26,44)(26,44)

Find the equation of the parabola of the form x=ay2+by+cx=a y^{2}+b y+cx=ay2+by+c that passes through the given three points. - (49,−1),(37,3),(93,10)(49,-1),(37,3),(93,10)(49,−1),(37,3),(93,10)

Graph the parabola. State the vertex of the parabola. - y=(x+4)2+3 y=(x+4)^{2}+3 y=(x+4)2+3

Find the midpoint of the line segment that connects the given points. - (−6,−1)(-6,-1)(−6,−1) and (7,8)(7,8)(7,8)

Solve the problem. -Arches in the shapes of parabolas are often used in construction. Find the equation of a parabolic arc that is 20 feet high at its highest point and 28 feet wide at the base, as illustrated in the figure. Place the origin at the midpoint of the base.

Solve the system by the substitution method. - 5x2−y2=105 x^{2}-y^{2}=105x2−y2=10 y=x2−2\mathrm{y}=\mathrm{x}^{2}-2y=x2−2

Find the standard-form equation of the ellipse. -

Graph the circle. State the center and radius of the circle - (x+3)2+(y−6)2=4(x+3)^{2}+(y-6)^{2}=4(x+3)2+(y−6)2=4

Graph the hyperbola. Give the coordinates of the center as well as the values of aaa and bbb . - x264−y29=1\frac{x^{2}}{64}-\frac{y^{2}}{9}=164x2​−9y2​=1

Solve. -An elliptical bicycle path is constructed in a local park. The equation of the ellipse that represents the path, in yards, is given by x21225+y24225=1\frac{\mathrm{x}^{2}}{1225}+\frac{\mathrm{y}^{2}}{4225}=11225x2​+4225y2​=1 . What are the length and the width of the bicycle path?

Graph the ellipse. Give the coordinates of the center, as well as the values of aaa and bbb . - 25x2+36y2=90025 x^{2}+36 y^{2}=90025x2+36y2=900

Find the distance between the pair of points. Round to the nearest tenth if necessary. - (−3,1)(-3,1)(−3,1) and (3,−7)(3,-7)(3,−7)

Find the standard-form equation of the hyperbola whose graph is shown. -

Find the center and radius of the circle by completing the square. - x2+y2−2x−10y+10=0x^{2}+y^{2}-2 x-10 y+10=0x2+y2−2x−10y+10=0

Graph the ellipse. Give the coordinates of the center, as well as the values of aaa and bbb . - 3x2+7y2−63=03 x^{2}+7 y^{2}-63=03x2+7y2−63=0

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Sequences, Series, and the Binomial Theorem

Filters

Solve the system by the substitution method. - $5 x^{2}-2 y^{2}=-12$ $4 \mathrm{x}^{2}+5 \mathrm{y}^{2}=96$

Graph the parabola. State the vertex of the parabola. - $y=-x^{2}-2 x-8$ $Graph the parabola. State the vertex of the parabola. - y=-x^{2}-2 x-8$

Solve the system by the substitution method. - $x^{2}+y^{2}=4$ $\mathrm{x}^{2}-\mathrm{y}^{2}=4$

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $(47,2)$ and $(26,44)$

Find the equation of the parabola of the form $x=a y^{2}+b y+c$ that passes through the given three points. - $(49,-1),(37,3),(93,10)$

Graph the parabola. State the vertex of the parabola. - $y=(x+4)^{2}+3$ $Graph the parabola. State the vertex of the parabola. - y=(x+4)^{2}+3$

Find the midpoint of the line segment that connects the given points. - $(-6,-1)$ and $(7,8)$

Solve the system by the substitution method. - $5 x^{2}-y^{2}=10$ $\mathrm{y}=\mathrm{x}^{2}-2$

Graph the circle. State the center and radius of the circle - $(x+3)^{2}+(y-6)^{2}=4$ $Graph the circle. State the center and radius of the circle - (x+3)^{2}+(y-6)^{2}=4$

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$ . - $\frac{x^{2}}{64}-\frac{y^{2}}{9}=1$ $Graph the hyperbola. Give the coordinates of the center as well as the values of a and b . - \frac{x^{2}}{64}-\frac{y^{2}}{9}=1$

Solve. -An elliptical bicycle path is constructed in a local park. The equation of the ellipse that represents the path, in yards, is given by $\frac{\mathrm{x}^{2}}{1225}+\frac{\mathrm{y}^{2}}{4225}=1$ . What are the length and the width of the bicycle path?

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$ . - $25 x^{2}+36 y^{2}=900$ $Graph the ellipse. Give the coordinates of the center, as well as the values of a and b . - 25 x^{2}+36 y^{2}=900$

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $(-3,1)$ and $(3,-7)$

Find the center and radius of the circle by completing the square. - $x^{2}+y^{2}-2 x-10 y+10=0$

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$ . - $3 x^{2}+7 y^{2}-63=0$ $Graph the ellipse. Give the coordinates of the center, as well as the values of a and b . - 3 x^{2}+7 y^{2}-63=0$