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

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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 .

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

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

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Sketching the Graph of a Parabola

       586–590 Sketch the graph of the parabola.

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Rewriting a Circle’s Equation in Standard Form

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

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