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Conic Sections Answers

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Consider the equation y – 4 = 2(x + 3)2. Where is the vertex located, and in which direction does the parabola open?

vertex: (–3, 4); parabola opens up

vertex: (–3, 4); parabola opens to the right

vertex: (3, –4); parabola opens up

vertex: (3, –4); parabola opens to the right

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Review the graph of circle A.

(x – 4)2 + (y + 5)2 = 12

(x + 4)2 + (y – 5)2 = 12

(x – 4)2 + (y + 5)2 = 36

(x + 4)2 + (y – 5)2 = 36

A parabola has the focus at (4, 6) and the directrix y = –6. Which equation represents this parabola?

(x – 4)2 = 24y

(x – 4)2 = y

(x – 4)2 = –24y

(x – 4)2 = y

The angle between the generator and the central axis of a double-napped cone is 50°. Which conic section is formed when a plane intersects the central axis at 50°?

circle

ellipse

parabola

hyperbola

Review the graph of circle A.

(x – 2)2 + y2 = 5

(x + 2)2 + y2 = 5

(x – 2)2 + y2 = 25

(x + 2)2 + y2 = 25

The equation (x + 1) = (y – 5)2 is represented by which graph?

On a coordinate plane, a parabola opens to the left. It goes through (negative 7, negative 3), has a vertex at (1, negative 5), and goes through (negative 7, negative 7).

On a coordinate plane, a parabola opens to the right. It goes through (7, 7), has a vertex at (negative 1, 5), and goes through (7, 3).

On a coordinate plane, a parabola opens to the right. It goes through (9, negative 3), has a vertex at (1, negative 5), and goes through (9, negative 7).

On a coordinate plane, a parabola opens to the left. It goes through (negative 9, 7), has a vertex at (negative 1, 5), and goes through (negative 9, 3).

Consider the equation (x – 5) = (y – 2)2. What is the equation of the directrix?

x = 4.0000

x = 4.7500

x = 4.6250

x = 4.9375

The angle between the generator and the central axis of a double-napped cone is 60°. A plane intersecting the cone makes an angle of 50° with the central axis. Which conic section is formed?

circle

ellipse

hyperbola

parabola

The center of a circle is 5 units below the origin, and the radius is 10 units. What is the equation of this circle?

x2 + (y + 5)2 = 10

(x + 5)2 + y2 = 10

x2 + (y + 5)2 = 100

(x + 5)2 + y2 = 100

Which graph represents the equation y = – (x – 1)2 + 1?

On a coordinate plane, a parabola opens up. It goes through (0, 2), has a vertex at (1, 1), and goes through (2, 2).

On a coordinate plane, a parabola opens down. It goes through (0, 0), has a vertex at (1, 1), and goes through (2, 0).

On a coordinate plane, a parabola opens down. It goes through (negative 2, 0), has a vertex at (negative 1, 1), and goes through (0, 0).

On a coordinate plane, a parabola opens up. It goes through (negative 2, 2), has a vertex at (negative 1, 1), and goes through (0, 2).

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