Question 1

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable.
-$\frac{x^{2}}{9}+\frac{y^{2}}{25}=1$

Accepted Answer

@#IMG-DLM& 
Ellipse;

Question 2

Write an equation for each of the following.
(a) The conic with center at the origin, focus at $(3,0)$ and $e=\frac{3}{2}$.
(b) The conic with focus at the origin, vertex at $(-5,0)$ and $e=1$.

Accepted Answer

The answer of Write an equation for each of the...

Question 3

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable.
-$x=t+2, y=-4 \sqrt{1-\frac{t^{2}}{25}}+5, t$ in $[0,5]$

Accepted Answer

@#IMG-DLM& 
Quarter Ellipse; c

Question 4

Match each equation on the left with the appropriate description of its graph on the right.
-$9(x-4)^{2}-4(y+3)^{2}=36$

Accepted Answer

A)  Ellipse; center $(-4,-3)$ 
B)  Parabola; opens right 
C)  Circle; center (4, -3$)$; radius 6 
D)  Parabola; opens upward 
E)  Circle; center $(-4,3)$; radius 6
F) Hyperbola; center $(4,-3)$ 
A)  Ellipse; center $(-4,-3)$ 
B)  Parabola; opens right 
C)  Circle; center (4, -3$)$; radius 6 
D)  Parabola; opens upward 
E)  Circle; center $(-4,3)$; radius 6
F) Hyperbola; center $(4,-3)$

Question 5

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable.
-$\frac{(x+2)^{2}}{36}+\frac{(y-1)^{2}}{16}=1$

Accepted Answer

@#IMG-DLM& 
Ellipse;

Question 6

The screen shown here gives the graph of $\frac{x^{2}}{9}+\frac{y^{2}}{36}=1$ as generated by a graphing calculator.
What two functions were used to obtain the graph?

Accepted Answer

The answer of The screen shown here gives the graph...

Question 7

The screen shown here gives the graph of $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$ as generated by a graphing calculator.
What two functions were used to obtain the graph?

Accepted Answer

The answer of The screen shown here gives the graph...

Question 8

A comet following a parabolic path with the Earth at the focus came within 8 million miles of the Earth. Position the Earth at the origin and the perihelion (closest) point of the orbit on the positive horizontal axis and determine the equation of the parabola. How far is the comet from Earth when it crosses the vertical axis?

Accepted Answer

The answer of A comet following a parabolic path with...

Question 9

Match each equation on the left with the appropriate description of its graph on the right.
-$4(x-6)^{2}+25(y-2)^{2}=100$

Accepted Answer

A)  Circle; center $(6,-2)$; radius 5 
B)  Hyperbola; center $(6,-2)$ 
C)  Parabola; opens left 
D)  Circle; center $(-6,2)$; radius 5 
E)  Parabola; opens downward
F) Ellipse; center $(6,2)$ 
A)  Circle; center $(6,-2)$; radius 5 
B)  Hyperbola; center $(6,-2)$ 
C)  Parabola; opens left 
D)  Circle; center $(-6,2)$; radius 5 
E)  Parabola; opens downward
F) Ellipse; center $(6,2)$

Question 10

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable
-$x^{2}+y^{2}-10 x+4 y+29=0$

Accepted Answer

@#IMG-DLM& 
Point (c

Question 11

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable.
-$x^{2}+y^{2}-10 x+4 y+13=0$

Accepted Answer

@#IMG-DLM& 
Circle;

Question 12

The screen shown here gives the graph of $\frac{x^{2}}{16}+\frac{y^{2}}{25}=1$ as generated by a graphing calculator.
What two functions were used to obtain the graph?

Accepted Answer

The answer of The screen shown here gives the graph...

Question 13

Match each equation on the left with the appropriate description of its graph on the right.
-$(x+3)^{2}+y=1$

Accepted Answer

A)  Ellipse; center $(3,1)$ 
B)  Hyperbola; center $(3,1)$ 
C)  Circle; center $(3,-1)$; radius 4 
D)  Parabola; opens downward 
E)  Circle; center $(-3,1)$; radius 4
F) Parabola; opens left 
A)  Ellipse; center $(3,1)$ 
B)  Hyperbola; center $(3,1)$ 
C)  Circle; center $(3,-1)$; radius 4 
D)  Parabola; opens downward 
E)  Circle; center $(-3,1)$; radius 4
F) Parabola; opens left

Question 14

Write an equation for each of the following.
(a) The conic with focus at the origin and vertex at $(0,3)$ and $e=1$.
(b) The conic with center at the origin, focus at $(-2,0)$ and $e=\frac{2}{3}$.

Accepted Answer

The answer of Write an equation for each of the...

Question 15

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable.
-$x=t-3, y=10 \sqrt{1-\frac{t^{2}}{36}}+2, t$ in $[-6,6]$

Accepted Answer

@#IMG-DLM& 
Half Ellipse; cent

Question 16

Graph $y=-3 \sqrt{1-\frac{x^{2}}{16}}$. Is the graph that of a function? Find the domain and range.

Accepted Answer

@#IMG-DLM& 
Yes. Dom

Question 17

Match each equation on the left with the appropriate description of its graph on the right.
-$(x-3)^{2}+4(y-1)^{2}=16$

Accepted Answer

A)  Ellipse; center $(3,1)$ 
B)  Hyperbola; center $(3,1)$ 
C)  Circle; center $(3,-1)$; radius 4 
D)  Parabola; opens downward 
E)  Circle; center $(-3,1)$; radius 4
F) Parabola; opens left 
A)  Ellipse; center $(3,1)$ 
B)  Hyperbola; center $(3,1)$ 
C)  Circle; center $(3,-1)$; radius 4 
D)  Parabola; opens downward 
E)  Circle; center $(-3,1)$; radius 4
F) Parabola; opens left

Question 18

Match each equation on the left with the appropriate description of its graph on the right.
-$(y+3)^{2}-x=-4$

Accepted Answer

A)  Ellipse; center $(-4,-3)$ 
B)  Parabola; opens right 
C)  Circle; center (4, -3$)$; radius 6 
D)  Parabola; opens upward 
E)  Circle; center $(-4,3)$; radius 6
F) Hyperbola; center $(4,-3)$ 
A)  Ellipse; center $(-4,-3)$ 
B)  Parabola; opens right 
C)  Circle; center (4, -3$)$; radius 6 
D)  Parabola; opens upward 
E)  Circle; center $(-4,3)$; radius 6
F) Hyperbola; center $(4,-3)$

Question 19

Match each equation on the left with the appropriate description of its graph on the right.
-$3(x-2)^{2}-(y-1)^{2}=9$

Accepted Answer

A)  Circle; center $(2,-1)$; radius 3 
B)  Hyperbola; center $(2,1)$ 
C)  Parabola; opens left 
D)  Circle; center $(-2,1)$; radius 3 
E)  Parabola; opens downward
F) Ellipse; center $(2,1)$ 
A)  Circle; center $(2,-1)$; radius 3 
B)  Hyperbola; center $(2,1)$ 
C)  Parabola; opens left 
D)  Circle; center $(-2,1)$; radius 3 
E)  Parabola; opens downward
F) Ellipse; center $(2,1)$

Question 20

Match each equation on the left with the appropriate description of its graph on the right.
-$(x+4)^{2}+(y-3)^{2}=36$

Accepted Answer

A)  Ellipse; center $(-4,-3)$ 
B)  Parabola; opens right 
C)  Circle; center (4, -3$)$; radius 6 
D)  Parabola; opens upward 
E)  Circle; center $(-4,3)$; radius 6
F) Hyperbola; center $(4,-3)$ 
A)  Ellipse; center $(-4,-3)$ 
B)  Parabola; opens right 
C)  Circle; center (4, -3$)$; radius 6 
D)  Parabola; opens upward 
E)  Circle; center $(-4,3)$; radius 6
F) Hyperbola; center $(4,-3)$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $\frac{x^{2}}{9}+\frac{y^{2}}{25}=1$

Write an equation for each of the following. (a) The conic with center at the origin, focus at $(3,0)$ and $e=\frac{3}{2}$ . (b) The conic with focus at the origin, vertex at $(-5,0)$ and $e=1$ .

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $x=t+2, y=-4 \sqrt{1-\frac{t^{2}}{25}}+5, t$ in $[0,5]$

Match each equation on the left with the appropriate description of its graph on the right. - $9(x-4)^{2}-4(y+3)^{2}=36$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $\frac{(x+2)^{2}}{36}+\frac{(y-1)^{2}}{16}=1$

Match each equation on the left with the appropriate description of its graph on the right. - $4(x-6)^{2}+25(y-2)^{2}=100$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable - $x^{2}+y^{2}-10 x+4 y+29=0$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $x^{2}+y^{2}-10 x+4 y+13=0$

Match each equation on the left with the appropriate description of its graph on the right. - $(x+3)^{2}+y=1$

Write an equation for each of the following. (a) The conic with focus at the origin and vertex at $(0,3)$ and $e=1$ . (b) The conic with center at the origin, focus at $(-2,0)$ and $e=\frac{2}{3}$ .

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $x=t-3, y=10 \sqrt{1-\frac{t^{2}}{36}}+2, t$ in $[-6,6]$

Graph $y=-3 \sqrt{1-\frac{x^{2}}{16}}$ . Is the graph that of a function? Find the domain and range.

Match each equation on the left with the appropriate description of its graph on the right. - $(x-3)^{2}+4(y-1)^{2}=16$

Match each equation on the left with the appropriate description of its graph on the right. - $(y+3)^{2}-x=-4$

Match each equation on the left with the appropriate description of its graph on the right. - $3(x-2)^{2}-(y-1)^{2}=9$

Match each equation on the left with the appropriate description of its graph on the right. - $(x+4)^{2}+(y-3)^{2}=36$

Linear Functions, Equations, and Inequalities

Analysis of Graphs of Functions

Polynomial Functions

Rational, Power, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Analytic Geometry and Nonlinear Systems

The Unit Circle and Functions of Trigonometry

Trigonometric Identities and Equations

Applications of Trigonometry and Vectors

Further Topics in Algebra

Limits, Derivatives, and Definite Integrals

Reference: Basic Algebraic Concepts

Filters

Exam 6: Systems and Matrices

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - x29+y225=1\frac{x^{2}}{9}+\frac{y^{2}}{25}=19x2​+25y2​=1

Write an equation for each of the following. (a) The conic with center at the origin, focus at (3,0)(3,0)(3,0) and e=32e=\frac{3}{2}e=23​ . (b) The conic with focus at the origin, vertex at (−5,0)(-5,0)(−5,0) and e=1e=1e=1 .

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - x=t+2,y=−41−t225+5,tx=t+2, y=-4 \sqrt{1-\frac{t^{2}}{25}}+5, tx=t+2,y=−41−25t2​​+5,t in [0,5][0,5][0,5]

Match each equation on the left with the appropriate description of its graph on the right. - 9(x−4)2−4(y+3)2=369(x-4)^{2}-4(y+3)^{2}=369(x−4)2−4(y+3)2=36

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - (x+2)236+(y−1)216=1\frac{(x+2)^{2}}{36}+\frac{(y-1)^{2}}{16}=136(x+2)2​+16(y−1)2​=1

The screen shown here gives the graph of x29+y236=1\frac{x^{2}}{9}+\frac{y^{2}}{36}=19x2​+36y2​=1 as generated by a graphing calculator. What two functions were used to obtain the graph?

The screen shown here gives the graph of x236+y216=1\frac{x^{2}}{36}+\frac{y^{2}}{16}=136x2​+16y2​=1 as generated by a graphing calculator. What two functions were used to obtain the graph?

Match each equation on the left with the appropriate description of its graph on the right. - 4(x−6)2+25(y−2)2=1004(x-6)^{2}+25(y-2)^{2}=1004(x−6)2+25(y−2)2=100

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable - x2+y2−10x+4y+29=0x^{2}+y^{2}-10 x+4 y+29=0x2+y2−10x+4y+29=0

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - x2+y2−10x+4y+13=0x^{2}+y^{2}-10 x+4 y+13=0x2+y2−10x+4y+13=0

The screen shown here gives the graph of x216+y225=1\frac{x^{2}}{16}+\frac{y^{2}}{25}=116x2​+25y2​=1 as generated by a graphing calculator. What two functions were used to obtain the graph?

Match each equation on the left with the appropriate description of its graph on the right. - (x+3)2+y=1(x+3)^{2}+y=1(x+3)2+y=1

Write an equation for each of the following. (a) The conic with focus at the origin and vertex at (0,3)(0,3)(0,3) and e=1e=1e=1 . (b) The conic with center at the origin, focus at (−2,0)(-2,0)(−2,0) and e=23e=\frac{2}{3}e=32​ .

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - x=t−3,y=101−t236+2,tx=t-3, y=10 \sqrt{1-\frac{t^{2}}{36}}+2, tx=t−3,y=101−36t2​​+2,t in [−6,6][-6,6][−6,6]

Graph y=−31−x216y=-3 \sqrt{1-\frac{x^{2}}{16}}y=−31−16x2​​ . Is the graph that of a function? Find the domain and range.

Match each equation on the left with the appropriate description of its graph on the right. - (x−3)2+4(y−1)2=16(x-3)^{2}+4(y-1)^{2}=16(x−3)2+4(y−1)2=16

Match each equation on the left with the appropriate description of its graph on the right. - (y+3)2−x=−4(y+3)^{2}-x=-4(y+3)2−x=−4

Match each equation on the left with the appropriate description of its graph on the right. - 3(x−2)2−(y−1)2=93(x-2)^{2}-(y-1)^{2}=93(x−2)2−(y−1)2=9

Match each equation on the left with the appropriate description of its graph on the right. - (x+4)2+(y−3)2=36(x+4)^{2}+(y-3)^{2}=36(x+4)2+(y−3)2=36

Linear Functions, Equations, and Inequalities

Analysis of Graphs of Functions

Polynomial Functions

Rational, Power, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Analytic Geometry and Nonlinear Systems

The Unit Circle and Functions of Trigonometry

Trigonometric Identities and Equations

Applications of Trigonometry and Vectors

Further Topics in Algebra

Limits, Derivatives, and Definite Integrals

Reference: Basic Algebraic Concepts

Filters

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $\frac{x^{2}}{9}+\frac{y^{2}}{25}=1$

Write an equation for each of the following. (a) The conic with center at the origin, focus at $(3,0)$ and $e=\frac{3}{2}$ . (b) The conic with focus at the origin, vertex at $(-5,0)$ and $e=1$ .

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $x=t+2, y=-4 \sqrt{1-\frac{t^{2}}{25}}+5, t$ in $[0,5]$

Match each equation on the left with the appropriate description of its graph on the right. - $9(x-4)^{2}-4(y+3)^{2}=36$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $\frac{(x+2)^{2}}{36}+\frac{(y-1)^{2}}{16}=1$

Match each equation on the left with the appropriate description of its graph on the right. - $4(x-6)^{2}+25(y-2)^{2}=100$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable - $x^{2}+y^{2}-10 x+4 y+29=0$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $x^{2}+y^{2}-10 x+4 y+13=0$

Match each equation on the left with the appropriate description of its graph on the right. - $(x+3)^{2}+y=1$

Write an equation for each of the following. (a) The conic with focus at the origin and vertex at $(0,3)$ and $e=1$ . (b) The conic with center at the origin, focus at $(-2,0)$ and $e=\frac{2}{3}$ .

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $x=t-3, y=10 \sqrt{1-\frac{t^{2}}{36}}+2, t$ in $[-6,6]$

Graph $y=-3 \sqrt{1-\frac{x^{2}}{16}}$ . Is the graph that of a function? Find the domain and range.

Match each equation on the left with the appropriate description of its graph on the right. - $(x-3)^{2}+4(y-1)^{2}=16$

Match each equation on the left with the appropriate description of its graph on the right. - $(y+3)^{2}-x=-4$

Match each equation on the left with the appropriate description of its graph on the right. - $3(x-2)^{2}-(y-1)^{2}=9$

Match each equation on the left with the appropriate description of its graph on the right. - $(x+4)^{2}+(y-3)^{2}=36$