Precalculus with Limits: A Graphing Approach, Sixth Edition
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Precalculus with Limits: A Graphing Approach, Sixth Edition View details
1. Conics: Circles and Parabolas
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Exercise 1 Page 643

We want to complete the sentence.

A is the intersection of a plane and a double-napped cone.

A plane that intersects a double-napped cone can create different geometric figures. For example, a plane that is perpendicular to the axis of the cones will create a circle.

If the plane is parallel to the axis of cones, the intersection is the hyperbola.

The intersection of the cones and the plane that is not perpendicular, nor parallel to the axis of the cones, creates a parabola or an ellipse.

The ellipse, circle, parabola, and hyperbola are four basic conic sections. Let's fill in the blank.

A conic section is the intersection of a plane and a double-napped cone.