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ОглавлениеChapter 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.
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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.
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Rewriting a Circle’s Equation in Standard Form
591–600 Write the equation of each circle in the standard form .
591.
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Identifying the Center and Radius of a Circle
601–605 Find the center and radius of each circle.
601.
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Sketching the Graph of a Circle
606–610 Sketch the graph of each circle, indicating the center and a point on the circle.
606.
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Writing an Ellipse’s Equation in Standard Form
611–620 Write the equation of each ellipse in the standard form .
611.
612.
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617.
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619.
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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.
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625.
Sketching the Graphs of Ellipses
626–630 Sketch the graph of the ellipse.
626.
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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.
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638.
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640.
Finding the Center, Foci, and Asymptotes of Hyperbolas
641–645 Determine the center, foci, and equations of the asymptotes of the hyperbola.
641.
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644.
645.
Sketching the Graphs of Hyperbolas
646–650 Sketch the graph of the hyperbola.
646.
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650.