Question 1

It is a type of conic where the set of all points (𝑥,𝑦) in a plane such that the difference of the distances between (𝑥,𝑦) and the foci (plural of focus) is a positive constant.

Accepted Answer

Hyperbola

Answer

Parabola

Answer

Circle

Answer

Ellipse

Question 2

It is a line segment that passes through the center of the hyperbola and has vertices as its endpoints.

Accepted Answer

Transverse Axis

Answer

Asymptotes

Answer

Foci

Answer

Conjugate Axis

Question 3

What do you call the line that is perpendicular to the transverse axis and has the co-vertices as its endpoints?

Accepted Answer

Conjugate Axis

Answer

Transverse Axis

Answer

Foci

Answer

Asymptotes

Question 4

What do you call the the midpoint of both the transverse and conjugate axes?

Accepted Answer

Center

Answer

Foci

Answer

Asymptotes

Answer

central rectangle

Question 5

A particular class of curves which oftentimes appear in nature and which have applications in other fields is called _______________.

Accepted Answer

Conic Sections

Answer

Coordinate Plane

Answer

Pi

Answer

Geometric Curves

Question 6

What is the standard equation of the hyperbola when it opens to the left and right?

Accepted Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Question 7

What is the standard equation of the hyperbola when it opens upward and downward?

Accepted Answer

$\frac{y^2}{a^2}\ -\frac{x^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Question 8

Which of these statements is true about hyperbolas?

Accepted Answer

Hyperbolas consist of two similar curves.

Answer

Hyperbolas cannot be graphed on a 2-dimensional grid.

Answer

Hyperbolas are the only member of the conic section category.

Answer

Hyperbolas are the set of all points an equal distance from the center.

Question 9

What must be true of the foci of a hyperbola?

Accepted Answer

The foci must lie on the transverse axis and be in the interior of the hyperbola.

Answer

The vertices of a hyperbola are the same points as the foci of a hyperbola.

Answer

They contain an asymptote.

Answer

Foci and vertices have different lines.

Question 10

What is the center of the hyperbola that has an equation of $\frac{y^2}{a^2}\ -\frac{x^2}{b^2}=1$ ?

Accepted Answer

(-5, 0)

Answer

(6, 5)

Answer

(0, 5)

Answer

(-4, 5)

Question 11

Given the equation $\frac{y^2}{a^2}\ -\frac{x^2}{b^2}=1$ ,what are the coordinates of its vertices?

Accepted Answer

(-3, 0) (3, 0)

Answer

(0, -5) (0, 5)

Answer

(-5, 0) (5, 0)

Answer

(0, -3) (0, 3)

Question 12

Given the equation $\frac{y^2}{a^2}\ -\frac{x^2}{b^2}=1$ , what are the coordinates of its foci?

Accepted Answer

(-4, 0) (4, 0)

Answer

(-5, 0) (5, 0)

Answer

(0, -4) (0, 4)

Answer

(0, -5) (0, 5)

Question 13

Given the equation $\frac{y^2}{a^2}\ -\frac{x^2}{b^2}=1$ , what are the equations of its asymptotes?

Accepted Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Question 14

Given the general equation $18x^2+18y^2-24x+48y-5=0$ , determine the type of conic section.

Accepted Answer

Circle

Answer

Ellipse

Answer

Hyperbola

Answer

Parabola

Question 15

Given the general equation $18x^2+18y^2-24x+48y-5=0$ , determine the type of conic section.

Accepted Answer

Ellipse

Answer

Circle

Answer

Parabola

Answer

Hyperbola

Question 16

Given the general equation $18x^2+18y^2-24x+48y-5=0$ , determine the type of conic section.

Accepted Answer

Hyperbola

Answer

Circle

Answer

Parabola

Answer

Ellipse

Question 17

Given the general equation $18x^2+18y^2-24x+48y-5=0$ , determine the type of conic section.

Accepted Answer

Parabola

Answer

Circle

Answer

Hyperbola

Answer

Ellipse

Question 18

Given the general equation $18x^2+18y^2-24x+48y-5=0$ , determine the type of conic section.

Accepted Answer

Hyperbola

Answer

Parabola

Answer

Circle

Answer

Ellipse

Question 19

A parabola opening to the left has an axis that contains the major axis of the ellipse $x^2+4y^2-10x-24y+45=0$ its focus is the center of the ellipse and the parabola passes through the covertices of the ellipse.

What is the standard form of the equation of the ellipse?

Accepted Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Question 20

A parabola opening to the left has an axis that contains the major axis of the ellipse $x^2+4y^2-10x-24y+45=0$ its focus is the center of the ellipse and the parabola passes through the covertices of the ellipse.

What are the coordinates of the center of the ellipse?

Accepted Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Question 21

A parabola opening to the left has an axis that contains the major axis of the ellipse $x^2+4y^2-10x-24y+45=0$ its focus is the center of the ellipse and the parabola passes through the covertices of the ellipse.

What is the value of b?

Accepted Answer

2

Answer

0

Answer

1

Answer

4

Question 22

A parabola opening to the left has an axis that contains the major axis of the ellipse $x^2+4y^2-10x-24y+45=0$ its focus is the center of the ellipse and the parabola passes through the covertices of the ellipse.

What are the coordinates of the covertices of the ellipse?

Accepted Answer

(5, 1) and (5, 5)

Answer

(-3, 3) and (-7, 3)

Answer

(5, -1) and (5, -5)

Answer

(3, 3) and (7, 3)

Question 23

A parabola opening to the left has an axis that contains the major axis of the ellipse $x^2+4y^2-10x-24y+45=0$ its focus is the center of the ellipse and the parabola passes through the covertices of the ellipse.

What are the coordinates of the vertex of the parabola?

Accepted Answer

(6, 3)

Answer

(-5, -3)

Answer

(5, 3)

Answer

(-6, -3)

Question 24

A parabola opening to the left has an axis that contains the major axis of the ellipse $x^2+4y^2-10x-24y+45=0$ its focus is the center of the ellipse and the parabola passes through the covertices of the ellipse.

What is the value of p?

Accepted Answer

1

Answer

0

Answer

2

Answer

4

Question 25

A parabola opening to the left has an axis that contains the major axis of the ellipse $x^2+4y^2-10x-24y+45=0$ its focus is the center of the ellipse and the parabola passes through the covertices of the ellipse.

What is the standard form of the equation of the parabola?

Accepted Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

Answer

$\frac{x^2}{a^2}\ -\frac{y^2}{b^2}=1$

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