Question 1

Solve the system by the substitution method.
-$64 x^{2}+81 y^{2}=5184$
$9 \mathrm{y}+8 \mathrm{x}=72$

Accepted Answer

A)  $(0,-9),(0,-8)$ 
B)  $(0,-8),(-9,0)$ 
C)  $(0,8),(9,0)$ 
D)  $(0,9),(8,0)$ 
A)  $(0,-9),(0,-8)$ 
B)  $(0,-8),(-9,0)$ 
C)  $(0,8),(9,0)$ 
D)  $(0,9),(8,0)$ C

Question 2

Find the midpoint of the line segment that connects the given points.
-$(2,9)$ and $(5,-7)$

Accepted Answer

A)  $(7,2)$ 
B)  $\left(\frac{7}{2}, 1\right)$ 
C)  $\left(-\frac{3}{2}, 8\right)$ 
D)  $(-3,16)$ 
A)  $(7,2)$ 
B)  $\left(\frac{7}{2}, 1\right)$ 
C)  $\left(-\frac{3}{2}, 8\right)$ 
D)  $(-3,16)$ B

Question 3

Find the equation of the parabola of the form $x=a y^{2}+b y+c$ that passes through the given three points.
-$(\mathrm{x}-2)^{2}=4(\mathrm{y}+5)$

Accepted Answer

A)  vertex: $(2,-5)$; focus $(2,-3)$; directrix $y=-7$
  
B)  vertex: (2, - 5); focus (2, - 4); directrix $y=-6$
  
C)  vertex: $ (2,-5) $; focus $ (2,-7) $; directrix $ y=-3 $
  
D)  vertex: $ (2,-5) $; focus $ (2,-6) $; directrix $ y=-4 $
  
A)  vertex: $(2,-5)$; focus $(2,-3)$; directrix $y=-7$
  
B)  vertex: (2, - 5); focus (2, - 4); directrix $y=-6$
  
C)  vertex: $ (2,-5) $; focus $ (2,-7) $; directrix $ y=-3 $
  
D)  vertex: $ (2,-5) $; focus $ (2,-6) $; directrix $ y=-4 $
  B

Question 4

Find the center and radius of the circle by completing the square.
-$x^{2}+y^{2}-16 x-6 y-8=0$

Accepted Answer

A)  $(-8,-3) ; r=81$ 
B)  $(-3,-8) ; r=81$ 
C)  $(8,3) ; r=9$ 
D)  $(3,8) ; r=9$ 
A)  $(-8,-3) ; r=81$ 
B)  $(-3,-8) ; r=81$ 
C)  $(8,3) ; r=9$ 
D)  $(3,8) ; r=9$

Question 5

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$.
-$y^{2}-9 x^{2}=81$

Accepted Answer

A)  center $ (0,0), a=9, b=3 $
  
B)  center $ (0,0), a=9, b=3 $
  
C)  center $ (0,0), a=3, b=9 $
  
D)  center $ (0,0), a=3, b=9 $
  
A)  center $ (0,0), a=9, b=3 $
  
B)  center $ (0,0), a=9, b=3 $
  
C)  center $ (0,0), a=3, b=9 $
  
D)  center $ (0,0), a=3, b=9 $

Question 6

Find the center and radius of the circle by completing the square.
-$x^{2}+y^{2}-6 x+16 y+9=0$

Accepted Answer

A)  $(8,-3) ; r=64$ 
B)  $(3,-8) ; r=8$ 
C)  $(-3,8) ; r=64$ 
D)  $(-8,3) ; r=8$ 
A)  $(8,-3) ; r=64$ 
B)  $(3,-8) ; r=8$ 
C)  $(-3,8) ; r=64$ 
D)  $(-8,3) ; r=8$

Question 7

Find the vertex of the parabola by completing the square.
-$y=x^{2}-3 x-9$

Accepted Answer

A)  $(1.5,-11.25)$ 
B)  $(-1.5,-9.25)$ 
C)  $(-1.5,-11.25)$ 
D)  $(1.5,6.75)$ 
A)  $(1.5,-11.25)$ 
B)  $(-1.5,-9.25)$ 
C)  $(-1.5,-11.25)$ 
D)  $(1.5,6.75)$

Question 8

Find the equation of the circle that has a diameter with the given endpoints.
-$(-6,6)$ and $(0,-2)$

Accepted Answer

A)  $(x-3)^{2}+(y+2)^{2}=25$ 
B)  $(x+3)^{2}+(y-2)^{2}=25$ 
C)  $(x+3)^{2}+(y-2)^{2}=5$ 
D)  $(x-3)^{2}+(y+2)^{2}=100$ 
A)  $(x-3)^{2}+(y+2)^{2}=25$ 
B)  $(x+3)^{2}+(y-2)^{2}=25$ 
C)  $(x+3)^{2}+(y-2)^{2}=5$ 
D)  $(x-3)^{2}+(y+2)^{2}=100$

Question 9

Find the foci of the ellipse. Round to the nearest tenth if necessary.
-$\frac{x^{2}}{289}+\frac{y^{2}}{64}=1$

Accepted Answer

A)  $(-19,0),(19,0)$ 
B)  $(-15,0),(15,0)$ 
C)  $(-17,0),(17,0)$ 
D)  $(-13,0),(13,0)$ 
A)  $(-19,0),(19,0)$ 
B)  $(-15,0),(15,0)$ 
C)  $(-17,0),(17,0)$ 
D)  $(-13,0),(13,0)$

Question 10

Most video games need to determine whether two objects touch, such as a character and a wall or a missile and an asteroid; this is known as collision detection. One method for doing this is to find a circle that bounds each object. If the distance between the centers of the two objects is less than or equal to the sum of the two radii of the circles that the objects are bounded by, the two objects are touching. Determine whether Object 1 with radius 112 pixels and center at $(432,195)$ touches Object 2 with radius 154 pixels and center at $(673,310)$.

Accepted Answer

A) True 
 B)False

Question 11

Solve the problem.
-A Ferris wheel has a diameter of 280 feet and the bottom of the Ferris wheel is 12 feet above the ground. Find the equation of the wheel if the origin is placed on the ground directly below the center of the wheel, as illustrated.

Accepted Answer

A)  $x^{2}+(y-140)^{2}=19,600$ 
B)  $\mathrm{x}^{2}+\mathrm{y}^{2}=19,600$ 
C)  $x^{2}+(y-140)^{2}=78,400$ 
D)  $x^{2}+(y-152)^{2}=19,600$ 
A)  $x^{2}+(y-140)^{2}=19,600$ 
B)  $\mathrm{x}^{2}+\mathrm{y}^{2}=19,600$ 
C)  $x^{2}+(y-140)^{2}=78,400$ 
D)  $x^{2}+(y-152)^{2}=19,600$

Question 12

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$.
-$\frac{(y-1)^{2}}{36}-\frac{x^{2}}{9}=1$

Accepted Answer

A)  center $ (1,0), a=3, b=6 $
  
B)  center $ (1,0), a=3, b=6 $
  
C)  center $ (0,1) a=3, b=6 $
  
D)  center $ (0,1), a=3, b=6 $
  
A)  center $ (1,0), a=3, b=6 $
  
B)  center $ (1,0), a=3, b=6 $
  
C)  center $ (0,1) a=3, b=6 $
  
D)  center $ (0,1), a=3, b=6 $

Question 13

Graph the circle. State the center and radius of the circle
-$(x+1)^{2}+(y+4)^{2}=4$

Accepted Answer

A)  center $(-1,4) ; r=2$
  
B)  center (1, - 4); $r=2$
  
C)  center $(1,4) ; r=2$
  
D)  center $(-1,-4) ; \mathrm{r}=2$
  
A)  center $(-1,4) ; r=2$
  
B)  center (1, - 4); $r=2$
  
C)  center $(1,4) ; r=2$
  
D)  center $(-1,-4) ; \mathrm{r}=2$

Question 14

Find the equation of the circle.
-$(x+4)^{2}+(y-2)^{2}=36$

Accepted Answer

A) 
  
B)   
C) 
  
D) 
  
A) 
  
B)   
C) 
  
D)

Question 15

Graph the circle. State the center and radius of the circle
-$x^{2}+(y-2)^{2}=16$

Accepted Answer

A)  center $ (0,-2) ; r=4 $
  
B)  center $ (2,0) ; r=4 $
  
C)  center $ (-2,0) ; r=4 $
  
D)  center $ (0,2) ; r=4 $
  
A)  center $ (0,-2) ; r=4 $
  
B)  center $ (2,0) ; r=4 $
  
C)  center $ (-2,0) ; r=4 $
  
D)  center $ (0,2) ; r=4 $

Question 16

Find the equation of the parabola of the form $y=a x^{2}+b x+c$ that passes through the given three points.
-$(-7,-35),(-6,-33),(-5,-35)$

Accepted Answer

A)  $y=-3 x^{2}-30 x+97$ 
B)  $y=-2 x^{2}-24 x-105$ 
C)  $y=-2 x^{2}-24 x+105$ 
D)  $y=-3 x^{2}-30 x-97$ 
A)  $y=-3 x^{2}-30 x+97$ 
B)  $y=-2 x^{2}-24 x-105$ 
C)  $y=-2 x^{2}-24 x+105$ 
D)  $y=-3 x^{2}-30 x-97$

Question 17

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$.
-$4 x^{2}+5 y^{2}-24 x+50 y+141=0$

Accepted Answer

A)  center $ (3,-5), \mathrm{a}=2, \mathrm{~b}=\sqrt{5} $
  
B)  center $ (-3,5), a=2, b=\sqrt{5} $
  
C)  center $ (-3,5), a=\sqrt{5}, b=2 $
  
D)  center $ (3,-5), a=\sqrt{5}, b=2 $
  
A)  center $ (3,-5), \mathrm{a}=2, \mathrm{~b}=\sqrt{5} $
  
B)  center $ (-3,5), a=2, b=\sqrt{5} $
  
C)  center $ (-3,5), a=\sqrt{5}, b=2 $
  
D)  center $ (3,-5), a=\sqrt{5}, b=2 $

Question 18

Solve the system by the substitution method.
-$y=13 x-x^{2}$
$5 x-y=-15$

Accepted Answer

A)  $(5,3)$ 
B)  $(-5,-10),(-3,0)$ 
C)  $(5,40),(3,30)$ 
D)  $(3,30)$ 
A)  $(5,3)$ 
B)  $(-5,-10),(-3,0)$ 
C)  $(5,40),(3,30)$ 
D)  $(3,30)$

Question 19

Most video games need to determine whether two objects touch, such as a character and a wall or a missile and an asteroid; this is known as collision detection. One method for doing this is to find a circle that bounds each object. If the distance between the centers of the two objects is less than or equal to the sum of the two radii of the circles that the objects are bounded by, the two objects are touching. Determine whether Object 1 with radius 9 pixels and center at $(5,30)$ touches Object 2 with radius 10 pixels and œenter at $(15,45)$.

Accepted Answer

A) True 
 B)False

Question 20

Find the center and radius of the circle by completing the square.
-$x^{2}-4 x+y^{2}-6 y+1=0$

Accepted Answer

A)  $(-2,-3) ; r=12$ 
B)  $(-2,-3) ; r=2 \sqrt{3}$ 
C)  $(2,3) ; r=12$ 
D)  $(2,3) ; r=2 \sqrt{3}$ 
A)  $(-2,-3) ; r=12$ 
B)  $(-2,-3) ; r=2 \sqrt{3}$ 
C)  $(2,3) ; r=12$ 
D)  $(2,3) ; r=2 \sqrt{3}$

Solve the system by the substitution method. - $64 x^{2}+81 y^{2}=5184$ $9 \mathrm{y}+8 \mathrm{x}=72$

Find the midpoint of the line segment that connects the given points. - $(2,9)$ and $(5,-7)$

Find the equation of the parabola of the form $x=a y^{2}+b y+c$ that passes through the given three points. - $(\mathrm{x}-2)^{2}=4(\mathrm{y}+5)$ $Find the equation of the parabola of the form x=a y^{2}+b y+c that passes through the given three points. - (\mathrm{x}-2)^{2}=4(\mathrm{y}+5)$

Find the center and radius of the circle by completing the square. - $x^{2}+y^{2}-16 x-6 y-8=0$

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$ . - $y^{2}-9 x^{2}=81$ $Graph the hyperbola. Give the coordinates of the center as well as the values of a and b . - y^{2}-9 x^{2}=81$

Find the center and radius of the circle by completing the square. - $x^{2}+y^{2}-6 x+16 y+9=0$

Find the vertex of the parabola by completing the square. - $y=x^{2}-3 x-9$

Find the equation of the circle that has a diameter with the given endpoints. - $(-6,6)$ and $(0,-2)$

Find the foci of the ellipse. Round to the nearest tenth if necessary. - $\frac{x^{2}}{289}+\frac{y^{2}}{64}=1$

Solve the problem. -A Ferris wheel has a diameter of 280 feet and the bottom of the Ferris wheel is 12 feet above the ground. Find the equation of the wheel if the origin is placed on the ground directly below the center of the wheel, as illustrated.

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$ . - $\frac{(y-1)^{2}}{36}-\frac{x^{2}}{9}=1$ $Graph the hyperbola. Give the coordinates of the center as well as the values of a and b . - \frac{(y-1)^{2}}{36}-\frac{x^{2}}{9}=1$

Graph the circle. State the center and radius of the circle - $(x+1)^{2}+(y+4)^{2}=4$ $Graph the circle. State the center and radius of the circle - (x+1)^{2}+(y+4)^{2}=4$

Find the equation of the circle. - $(x+4)^{2}+(y-2)^{2}=36$

Graph the circle. State the center and radius of the circle - $x^{2}+(y-2)^{2}=16$ $Graph the circle. State the center and radius of the circle - x^{2}+(y-2)^{2}=16$

Find the equation of the parabola of the form $y=a x^{2}+b x+c$ that passes through the given three points. - $(-7,-35),(-6,-33),(-5,-35)$

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$ . - $4 x^{2}+5 y^{2}-24 x+50 y+141=0$ $Graph the ellipse. Give the coordinates of the center, as well as the values of a and b . - 4 x^{2}+5 y^{2}-24 x+50 y+141=0$

Solve the system by the substitution method. - $y=13 x-x^{2}$ $5 x-y=-15$

Find the center and radius of the circle by completing the square. - $x^{2}-4 x+y^{2}-6 y+1=0$

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

Solve the system by the substitution method. - 64x2+81y2=518464 x^{2}+81 y^{2}=518464x2+81y2=5184 9y+8x=729 \mathrm{y}+8 \mathrm{x}=729y+8x=72

Find the midpoint of the line segment that connects the given points. - (2,9)(2,9)(2,9) and (5,−7)(5,-7)(5,−7)

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. - (x−2)2=4(y+5)(\mathrm{x}-2)^{2}=4(\mathrm{y}+5)(x−2)2=4(y+5)

Find the center and radius of the circle by completing the square. - x2+y2−16x−6y−8=0x^{2}+y^{2}-16 x-6 y-8=0x2+y2−16x−6y−8=0

Graph the hyperbola. Give the coordinates of the center as well as the values of aaa and bbb . - y2−9x2=81y^{2}-9 x^{2}=81y2−9x2=81

Find the center and radius of the circle by completing the square. - x2+y2−6x+16y+9=0x^{2}+y^{2}-6 x+16 y+9=0x2+y2−6x+16y+9=0

Find the vertex of the parabola by completing the square. - y=x2−3x−9y=x^{2}-3 x-9y=x2−3x−9

Find the equation of the circle that has a diameter with the given endpoints. - (−6,6)(-6,6)(−6,6) and (0,−2)(0,-2)(0,−2)

Find the foci of the ellipse. Round to the nearest tenth if necessary. - x2289+y264=1\frac{x^{2}}{289}+\frac{y^{2}}{64}=1289x2​+64y2​=1