Precalculus Conic Sections

Write an equation for an ellipse with the given characteristics: length of major axis = 12; foci at (-2, 1) (-2, -9)

Write an equation for an ellipse with the given characteristics: vertices at (7, -4) (-3, -4); foci at (6, -4) (-2, -4)

Why are Conic Sections given this name?

• They are the cross-sections given when a cone is sliced.

• Because it's part of 'da rules'

• They are the cross-sections given when any 3D image is sliced.

What is the equation of the circle shown in the graph?

Mathematical Equivalence

ON

Which of the following statements are NOT true

• The minor axis of a vertical ellipse is vertical

• The transverse axis of a horizontal hyperbola is horizontal.

• Another name for the transverse axis of a hyperbola is the minor axis.

• If the equation of a circle is: x² + y² = 8, the diameter of the circle is 16.

• The parabola 12y = 6x² -30 opens up

A telescope is built using a hyperbolic mirror modeled by the equation and a parabolic mirror that open downward. The parabola has the vertex (-1, -4) and shares a focus with the hyperbola. What are the coordinates of the focus they share?

• (-1, -4)

• (4, -1)

• (-1, 6)

• (-6, -1)

Which of the following are true?

• A parabola has 2 foci.

• A circle's diameter is equal to it's radius squared

• A hyperbola uses a²+b²=c²

• An ellipse uses a²+b²=c²

• The distance from the center to a vertex along the transverse axis is 'a' in a hyperbola

Write an equation for the hyperbola with the given characteristics: foci (8, 0) (8, 8); vertices (8, 2) (8, 6)