Mary Jane Sterling - Algebra II - 1001 Practice Problems For Dummies (+ Free Online Practice)

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Chapter 10

Conic sections get this designation because they can all be described using slices of cones. The most familiar conic section is the circle. Our planets follow elliptical orbits, and comets follow hyperbolic orbits. That leaves the parabola to reflect upon — it’s the shape of the reflector plates in your car’s headlights.

In this chapter, you’ll work with the different conic sections in the following ways:

Writing the equations of parabolas in their standard form

Picking out the vertex, focus, directrix, and axis of symmetry from the standard equation of a parabola

Sketching parabolas

Writing the equations of circles in their standard form

Picking out the center and radius from the standard equation of a circle

Sketching circles

Writing the equations of ellipses in their standard form

Picking out the center, foci, and axes from the standard equation of an ellipse

Sketching ellipses

Writing the equations of hyperbolas in their standard form

Picking out the center, foci, and axes from the standard equation of a hyperbola

Sketching hyperbolas

Don’t let common mistakes trip you up; watch for the following when working with conic sections and their standard equations:

Recognizing which standard form to apply to a general equation

Completing the square correctly to write the standard equation

Finding square roots when using the standard form to sketch conic sections

571–580 Write the equation of the parabola in standard form, either .

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581–585 Identify the vertex, focus, directrix, and axis of symmetry of each parabola.

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586–590 Sketch the graph of the parabola.

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591–600 Write the equation of each circle in the standard form .

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