562.
563.
564.
565.
566.
567.
568.
569.
570.
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.
