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Math 1021 Section 2.2

Math 1021 Section 2.2 - A x 2 Ay 2 B x Cy D = 0 where A B C...

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Math 1021 Section 2.2 Circles A circle is a set of points that are a fixed distance from a fixed point. The fixed distance is the radius , r, of the circle and the fixed point, (h, k), is the center of the circle. Standard Form of an Equation of a Circle: (x – h) 2 + (y – k) 2 = r 2 where (h, k) = center of the circle, and r = radius of the circle. Note: This equation of a circle comes from using the distance formula between the center of the circle and any point on the circle will be equal to the radius. If you were to eliminate the parentheses above by squaring (x – h) and (y – k), this will lead you to the General Form (see below). General Form of an Equation of a Circle:

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Unformatted text preview: A x 2 + Ay 2 +B x + Cy + D = 0, where A, B, C, and D are real numbers. Ex. 1: Given r = 2; (h, k) = (-3, 1) a.) Write the standard form of the equation of the circle. b.) Write the general form of the equation of the circle. 10 8 6 4 2-2-4-6-8-15-10-5 5 10 15 r (x, y) (h, k) Ex. 2: Find the center and radius of the circle, any intercepts, then graph the circle. a.) (x – 3) 2 + ( y + 1) 2 = 16 b.) 2 x 2 +2y 2 +16x - 8y + 32 = 0 Ex. 3: Find the standard form of the equation of the circle with a.) center at the point (-5, 6) and tangent to the y-axis. b.) with endpoints of a diameter at the points (4, 3) and (0, 1)....
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Math 1021 Section 2.2 - A x 2 Ay 2 B x Cy D = 0 where A B C...

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