10 Chapter Review

Connecting BIG ideas and Answering the Essential Questions

1 Modeling The intersection of a cone and a plane parallel to the side of a cone is a parabola.	Parabolas (Lesson 10-2) Centered at the origin, a parabola has equation y = a x 2 , y equals , eh x squared , comma  or x = a y 2 . x equals , eh y squared , .	Translating Conic Sections (Lesson 10-6) Centered at (h, k), substitute x − h x minus h  for x and y − k y minus k  for y in the original equation for a conic section. Image Long Description
2 Equivalence x 2 9 + y 2 9 = 1 fraction x squared , over 9 end fraction , plus , fraction y squared , over 9 end fraction , equals 1  is an equation of a circle centered at the origin with radius 3. Multiply each side by 9 to get x 2 + y 2 = 9 . x squared , plus . y squared , equals 9 .	Circles (Lesson 10-3) Centered at the origin, a circle with radius r has equation x 2 + y 2 = r 2 . x squared , plus , y squared , equals , r squared , .
3 Coordinate Geometry The x 2 x squared  and y 2 y squared  terms of the algebraic form of an ellipse are both positive. For a hyperbola, one term is negative.	Ellipses and Hyperbolas (Lessons 10-4 and 10-5) Centered at the origin, an ellipse has equation x 2 a 2 + y 2 b 2 = 1 fraction x squared , over eh squared end fraction . plus . fraction y squared , over b squared end fraction . equals 1 a hyperbola has equation x 2 a 2 − y 2 b 2 = 1  or  y 2 a 2 − x 2 b 2 = 1 . fraction x squared , over eh squared end fraction . minus . fraction y squared , over b squared end fraction . equals 1 , or . fraction y squared , over eh squared end fraction . minus . fraction x squared , over b squared end fraction . equals 1 .

Chapter Vocabulary

• axis of symmetry (p. 646)
• center of a circle (p. 630)
• center of a hyperbola (p. 646)
• center of an ellipse (p. 639)
• circle (p. 630)
• conic section (p. 614)
• conjugate axis (p. 646)
• co-vertices of an ellipse (p. 639)
• directrix (p. 622)
• ellipse (p. 638)
• focal length (p. 622)
• focus of a parabola (p. 622)
• foci of an ellipse (p. 638)
• foci of a hyperbola (p. 645)
• hyperbola (p. 645)
• major axis (p. 639)
• minor axis (p. 639)
• radius (p. 630)
• standard form of an equation of a circle (p. 630)
• transverse axis (p. 646)
• vertices of an ellipse (p. 639)
• vertices of a hyperbola (p. 646)

Fill in the blanks.

1. In the definition of a parabola, a point on the curve is equidistant from the focus and the ?.
2. The vertices of an ellipse are on its ?.
3. ( x − h ) 2 + ( y − k ) 2 = r 2 open x minus h close squared . plus . open y minus k close squared . equals , r squared  is the ?.
4. The distance from a point on a circle to its center is the ? of the circle.
5. The vertices of a hyperbola are on its ?.

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