Question 1

Given the parabola $$y - 32 = -16x + 1$$, what is the equation of its axis of symmetry?

Accepted Answer

$$x = 1$$

Question 2

For the parabola $$x^2 - 4x - 4y - 4 = 0$, what are the coordinates of its vertex?

Accepted Answer

$$(2, -2)$$

Question 3

A parabola has its vertex at $$(1, -3)$$ and its focus at $$(1, -1). $$What is its standard form equation?

Accepted Answer

$$(x - 1)^2$ = 8(y + 3)$$

Question 4

Given the ellipse $$y - 229 + x + 124 = 1$$, what is the center of the ellipse?

Accepted Answer

$$(-124, 229)$$

Question 5

For the ellipse $$4x^2$$ + $$9y^2 - 16x - 20 = 0$, what is the length of its major axis?

Accepted Answer

$$6$$

Question 6

An ellipse has its center at $$(1, -2)$$, a vertex at $$(1, 0)$$, and a minor axis intersection at $$(0, -2). $$What is its standard form equation?

Accepted Answer

$$\frac{(x-1)^2$}{1^2$} + \frac{(y+2)^2$}{2^2$} = 1$$

Question 7

Given the hyperbola $$x - 225 - y28 = 1$$, what is the equation of its transverse axis?

Accepted Answer

$$x = 0$$

Question 8

For the hyperbola $$5x^2$$ - $$4y^2 + 10x + 8y - 19 = 0$, what are the coordinates of its center?

Accepted Answer

$$(-1, -1)$$

Question 9

A hyperbola has its center at $$(1, -2)$$, a focus at $$(4, -2)$$, and a vertex at $$(3, -2). $$What is its standard form equation?

Accepted Answer

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

Question 10

Which of the following best describes the latus rectum of a parabola?

Accepted Answer

A line segment perpendicular to the axis of symmetry, passing through the focus, with endpoints on the parabola

Question 11

Given the ellipse $$4x^2$$ + $$9y^2 - 16x - 20 = 0$, what is the equation of its major axis?

Accepted Answer

$$y = -1$$

Question 12

For the hyperbola $$5x^2$$ - $$4y^2 + 10x + 8y - 19 = 0$, what is the equation of one of its asymptotes?

Accepted Answer

$$y + 1 = \pm \sqrt{\frac{5}{4}} (x + 1)$$

Question 13

A satellite dish is shaped like a paraboloid. If its cross-section is described by $$(x - 1)^2$ = 8(y + 3)$$, what is the distance from the vertex to the focus?

Accepted Answer

$$2$$

Question 14

Given the ellipse $$4x^2$$ + $$9y^2 - 16x - 20 = 0$, what are the coordinates of its center?

Accepted Answer

$$(2, 0)$$

Question 15

For the hyperbola $$x - 225 - y28 = 1$$, what is the equation of one of its asymptotes?

Accepted Answer

$$y = x$$

Question 16

Which of the following statements is true about the directrix of a parabola?

Accepted Answer

It is a line perpendicular to the axis of symmetry and equidistant from the vertex as the focus but on the opposite side

Question 17

If an ellipse has its center at $$(1, -2)$$ and a vertex at $$(1, 0)$$, what is the value of $$a ($$the semi-major axis length)?

Accepted Answer

$$2$$

Question 18

Given the hyperbola $$5x^2$$ - $$4y^2 + 10x + 8y - 19 = 0$, what is the distance between its vertices?

Accepted Answer

$$2 \sqrt{5}$$

Question 19

A parabola opens upward and has its vertex at $$(2, -2). If $$its focus is at $$(2, 0)$$, what is the equation of its directrix?

Accepted Answer

$$y = -4$$

Question 20

Which of the following best describes the relationship between the foci and vertices of an ellipse?

Accepted Answer

The foci are always inside the ellipse along the major axis, and the sum of the distances from any point on the ellipse to the two foci is constant

Step-by-Step Guidance for Conic Sections: Parabolas, Ellipses, and Hyperbolas

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