Quiz about Precalculus Conic Sections

Question 1

Write an equation for an ellipse with the given characteristics: length of major axis = 12; foci at (-2, 1) (-2, -9)

Accepted Answer

$$\frac{\left(x+2\right)^2}{11}+\frac{\left(y+4\right)^2}{36}=1$$

Answer

$$\frac{\left(x-3\right)^2}{25}+\frac{\left(y+6\right)^2}{9}=1$$

Answer

$$\frac{\left(x+4\right)^2}{11}+\frac{\left(y+2\right)^2}{64}=1$$

Answer

$$\frac{\left(x-2\right)^2}{25}-\frac{\left(y+4\right)^2}{36}=1$$

Question 2

Write an equation for an ellipse with the given characteristics: vertices at (7, -4) (-3, -4); foci at (6, -4) (-2, -4)

Accepted Answer

$$\frac{\left(x-2\right)^2}{25}+\frac{\left(y+4\right)^2}{9}=1$$

Answer

$$\frac{\left(x-2\right)^2}{16}+\frac{\left(y-4\right)^2}{9}=1$$

Answer

$$\frac{\left(x-2\right)^2}{25}-\frac{\left(y+4\right)^2}{9}=1$$

Answer

$$\frac{\left(x+2\right)^2}{9}+\frac{\left(y+4\right)^2}{25}=1$$

Question 3

Write an equation for the hyperbola with the given characteristics: vertices (3, 0) (-3, 0); asymptotes $$y=\pm\frac{2}{3}x$$

Accepted Answer

$$\frac{x^2}{9}-\frac{y^2}{4}=1$$

Answer

$$\frac{x^2}{3}-\frac{y^2}{5}=1$$

Answer

$$\frac{x^2}{64}-\frac{y^2}{25}=1$$

Answer

$$\frac{y^2}{4}-\frac{x^2}{16}=1$$

Question 4

Why are Conic Sections given this name?

Accepted Answer

They are the cross-sections given when a cone is sliced.

Answer

Because it's part of 'da rules'

Answer

They are the cross-sections given when any 3D image is sliced.

Question 5

Which of the following statements are NOT true

Accepted Answer

The minor axis of a vertical ellipse is vertical

Accepted Answer

Another name for the transverse axis of a hyperbola is the minor axis.

Accepted Answer

If the equation of a circle is: x² + y² = 8, the diameter of the circle is 16.

Answer

The transverse axis of a horizontal hyperbola is horizontal.

Answer

The parabola 12y = 6x² -30 opens up

Question 6

A telescope is built using a hyperbolic mirror modeled by the equation and a parabolic mirror that open downward. The parabola has the vertex (-1, -4) and shares a focus with the hyperbola. What are the coordinates of the focus they share?

Accepted Answer

(-1, 6)

Answer

(-1, -4)

Answer

(4, -1)

Answer

(-6, -1)

Question 7

Which of the following are true?

Accepted Answer

A hyperbola uses a²+b²=c²

Accepted Answer

The distance from the center to a vertex along the transverse axis is 'a' in a hyperbola

Answer

A parabola has 2 foci.

Answer

A circle's diameter is equal to it's radius squared

Answer

An ellipse uses a²+b²=c²

Question 8

Write an equation for the hyperbola with the given characteristics: foci (8, 0) (8, 8); vertices (8, 2) (8, 6)

Accepted Answer

$$\frac{\left(y-4\right)^2}{4}-\frac{\left(x-8\right)^2}{12}=1$$

Answer

$$\frac{\left(y-4\right)^2}{2}-\frac{\left(x-5\right)^2}{7}=1$$

Answer

$$\frac{\left(y-5\right)^2}{4}-\frac{\left(x-2\right)^2}{12}=1$$

Question 9

Which ellipse has the greatest eccentricity?

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 10

Write an equation for a parabola with the given focus F and vertex V:

F(2, 8) V(2, 10)

Accepted Answer

$$\left(x-2\right)^2=-8\left(y-10\right)$$

Answer

$$\left(x-4\right)^2=-8\left(y+10\right)$$

Answer

$$\left(x-2\right)^2=-6\left(y-5\right)$$

Answer

$$\left(x-3\right)^2=-5\left(y+10\right)$$

Question 11

Write an equation for a parabola with the given focus F and vertex V: F(2, 5) V(-1, 5)

Accepted Answer

$$\left(y-5\right)^2=12\left(x+1\right)$$

Answer

$$\left(y-5\right)^2=-12\left(x+1\right)$$

Answer

$$\left(x-5\right)^2=8\left(y+1\right)$$

Answer

$$\left(y+5\right)^2=-12\left(x-1\right)$$

Question 12

Graph the ellipse: $$\frac{\left(x-5\right)^2}{49}+\frac{\left(y+3\right)^2}{9}=1$$

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 13

These are curves obtained by intersecting a plane and a right circular cone.

Accepted Answer

Conic Sections

Answer

Cross Sections

Answer

Circles

Answer

Parabolas

Question 14

Which type of conic section is this equation?

Accepted Answer

circle

Answer

ellipse

Answer

hyperbola

Answer

parabola

Question 15

Which type of conic section is this equation?

Accepted Answer

circle

Answer

ellipse

Answer

hyperbola

Answer

parabola

Question 16

Q1. What is the shape of a conic section?

Accepted Answer

A) Circle

Answer

B) Ellipse

Answer

C) Parabola

Answer

D) Hyperbola

Question 17

Question 17.

Accepted Answer

Parabola

Answer

Circle

Answer

Ellipse

Answer

Hyperbola

Question 18

Identify the conic represented by the graph.

Accepted Answer

<html><head></head><body>Circle</body></html>

Answer

<html><head></head><body>Parabola</body></html>

Answer

<html><head></head><body>Hyperbola</body></html>

Answer

<html><head></head><body>Ellipse</body></html>

Precalculus Conic Sections

20 questions

Write an equation for an ellipse with the given characteristics: length of major axis = 12; foci at (-2, 1) (-2, -9)

Write an equation for an ellipse with the given characteristics: vertices at (7, -4) (-3, -4); foci at (6, -4) (-2, -4)

Why are Conic Sections given this name?

What is the equation of the circle shown in the graph?

Which of the following statements are NOT true

A telescope is built using a hyperbolic mirror modeled by the equation and a parabolic mirror that open downward. The parabola has the vertex (-1, -4) and shares a focus with the hyperbola. What are the coordinates of the focus they share?

Which of the following are true?

Write an equation for the hyperbola with the given characteristics: foci (8, 0) (8, 8); vertices (8, 2) (8, 6)

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