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Post1330_section8o2a

Post1330_section8o2a - 29 7 3 2 2 = y x Sometimes the...

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Section 8.2a - Circles 1 Section 8.2a Circles To form a conic section, we’ll take this double cone and slice it with a plane. When we do this, we’ll get one of several different results. A circle, an ellipse, a parabola, or a hyperbola. http://mrhiggins.net/algebra2/wp-content/uploads/2008/05/allconics.jpg You may also get what are called degenerate conic sections. As we study conic sections, we will be looking at special cases of the general second-degree equation: 0 2 2 = + + + + + F Ey Dx Cy Bxy Ax . The Circle A circle is the set of all points that are equidistant from a fixed point. The fixed point is called the center and the distance from the center to any point on the circle is called the radius . The standard form of the equation of a circle is ( ( 2 2 2 r k y h x = - + - , where the center of the circle is the point ( k h , and the radius is r .

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Section 8.2a - Circles 2 Example 1: State the center and the radius of the circle
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Unformatted text preview: ( 29 7 3 2 2 = + + y x . Sometimes the equation will be given in the general form, and your first step will be to rewrite the equation in the standard form. You’ll need to complete the square to do this. Example 2: Write the equation in standard form then find the center and the radius. 26 44 10 6 2 2 = +-+ + y x y x Example 3: Write the equation in standard form then find the center and the radius. 20 10 20 5 5 2 2 = + + +-+ + + y x y x We can also write the equation of a circle, given appropriate information. Example 4: Write the equation of the circle with center (-5, 2) and has radius 5 3 . Section 8.2a - Circles 3 Example 5: Write an equation of a circle with center (1, 3) which passes through the point (4, -7). Example 6: Write an equation of a circle if the endpoints of the diameter of the circle are (6, -3) and (-4, 7)....
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