AnswersPrecalculusConic Sections

Conic Sections Answers

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The angle between the generator and the central axis of a double-napped cone is 40°. A plane intersects the central axis at an angle between 40° and 90°. Which conic section is formed?

A
circle
B
ellipse
C
hyperbola
D
parabola
2
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Which graph represents the equation y = – (x – 1)2 + 1?

A
On a coordinate plane, a parabola opens up. It goes through (0, 2), has a vertex at (1, 1), and goes through (2, 2).
Option A
B
On a coordinate plane, a parabola opens down. It goes through (0, 0), has a vertex at (1, 1), and goes through (2, 0).
Option B
C
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).
Option C
D
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).
Option D
3

Review the graph of a parabola.

Question illustration
A
2(x + 2) = (y + 3)2
B
2(y + 2) = (x + 3)2
C
–2(y + 2) = (x + 3)2
D
–2(x + 2) = (y + 3)2
4

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

Question illustration
A
x = 4.0000
B
x = 4.7500
C
x = 4.6250
D
x = 4.9375

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