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If the vertex is (1, 2) and the directrix is y = 7, what is the focus?

(1, -3)

Solve the system algebraically.

(2, 10) (-2, -10)

Write the standard-form equation of the circle that has a diameter with endpoints (-44, -7) and (4, 7).

(x + 20)2 + y2 = 625

Which of the following equations could represent the graph?

(x + 3)2 + (y + 3)2 = 9

Which of the following equations could represent the graph? two lines one above x axis one below x axis

(y - 2)^2/4 - (x - 2)^2/64 = 1

What are the numbers of possible solutions to a system of an ellipse and a hyperbola if they have the same center? Select all that apply.

0, 2

Two different circles can intersect in a maximum of _____ points.

2

Which of the following are equations of a circle? Select all that apply.

2x2 + 2y2 - 3x = 9; x2 + y2 + 4x - 6y = 12

Which of the following are equations of ellipses? Select all that apply.

3(x + 2)^2 + (y + 1)^2 = 5; (x - 3)^2 = 7 - 4(y + 2)^2; 4x^2 + 8x +8y^2 + 12y = 5

State the center and radius of (x - 7)2 + (y + 3)2 = 9.

C(7, -3), r = 3

The major axis of the ellipse is horizontally stretched.

False

Describe how the graph of the equation changes when a = b.

The ellipse turns into a circle.

A system involving two different conic equations can have at most four solutions.

True

Identify the conic represented by x2 + 8x + y2 - 6y - 11 = 0.

circle

The plane is perpendicular to the axis and does not contain the vertex.

circle

Which of the following ellipses has the smallest eccentricity?

circle

The plane is not perpendicular to the axis or parallel to any element and intersects only one nappe.

ellipse

Identify the conic represented by 3x2 - 5y2 - 18x + 20y + 22 = 0.

hyperbola

The plane is parallel to the axis.

hyperbola

Give the standard-form equation of the parabola whose vertex is at the origin and whose focus is (0, 8).

none of the above

Identify the conic represented by 2y2 - x + 8y + 1 = 0.

parabola

The plane is parallel to an element of the surface.

parabola

The plane contains the axis.

two intersecting lines

State the vertex, focus, and directrix of y = -2(x + 1)2 + 3.

vertex: (-1, 3); focus: (-1, 2 7/8); directrix: y = 3 1/8

Write the standard-form equation of the parabola with directrix x = 1 and focus (3, 4).

x = 1/4 (y - 4)2 + 2

Write a standard-form equation of an ellipse with foci (±12, 0) and co-vertices (0, ±5).

x^2/169 + y^2/25 = 1

Which of the following could be the equation of the following graph? Consider the vertex, the y-intercept, and zeros.

y = -(x - 2)2 + 9

Find the standard-form equation of a hyperbola of eccentricity e = 1.25 with center at the origin and vertex (0, 8).

y^2/64 - x^2/36 = 1


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