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Chapter 10

Conic Sections

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.

The Problems You’ll Work On

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

What to Watch Out For

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

Rewriting Equations of Parabolas in Standard Form

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

571.

572.

573.

574.

575.

576.

577.

578.

579.

580.

Determining a Vertex, Focus, Directrix, and Axis of Symmetry

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

581.

582.

583.

584.

585.

Sketching the Graph of a Parabola

586–590 Sketch the graph of the parabola.

586.

587.

588.

589.

590.

Rewriting a Circle’s Equation in Standard Form

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

591.

592.

593.

594.

595.

596.

597.

598.

599.

600.

Identifying the Center and Radius of a Circle

601–605 Find the center and radius of each circle.

601.

602.

603.

604.

605.

Sketching the Graph of a Circle

606–610 Sketch the graph of each circle, indicating the center and a point on the circle.

606.

607.

608.

609.

610.

Writing an Ellipse’s Equation in Standard Form

611–620 Write the equation of each ellipse in the standard form .

611.

612.

613.

614.

615.

616.

617.

618.

619.

620.

Identifying the Center, the Foci, and Axis Endpoints

621–625 Determine the center, the foci, and the endpoints of the major axis and minor axis of the ellipses.

621.

622.

623.

624.

625.

Sketching the Graphs of Ellipses

626–630 Sketch the graph of the ellipse.

626.

627.

628.

629.

630.

Writing the Equation of a Hyperbola in Standard Form

631–640 Write the equation of each hyperbola in standard form, either or .

631.

632.

633.

634.

635.

636.

637.

638.

639.

640.

Finding the Center, Foci, and Asymptotes of Hyperbolas

641–645 Determine the center, foci, and equations of the asymptotes of the hyperbola.

641.

642.

643.

644.

645.

Sketching the Graphs of Hyperbolas

646–650 Sketch the graph of the hyperbola.

646.

647.

648.

649.

650.

Algebra II: 1001 Practice Problems For Dummies (+ Free Online Practice)

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