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Advanced Math Name _____________________________ Circles Practice Mini-Quiz 1. 2. Find the center and radius: ( x + 3)2 + (y ! 2)2 = 7 center: (-3, 2) radius: 7 Find the center and radius: x 2 ! 4x + y 2 + 8y ! 2 = 0 x 2 ! 4x + 4 + y 2 + 8y +16 = 2 + 4 +16 (x ! 2)2 + (y + 4)2 = 22 center: (2, –4) 3. radius: 22 Find the equation of a circle with endpoints of a diameter (5, 1) and (–3, 7). " 5 + !3 1 + 7 % , ' = (1, 4) 2 2 & 2 2 2 equation so far: (x !1) + (y ! 4) = r (5 !1)2 + (1 ! 4)2 = r 2 center is midpoint: $ # 2 plug in a point on the circle to find r : 16 + 9 = r 2 r 2 = 25 2 replace r with 25: 4. (x !1)2 + (y ! 4)2 = 25 Find the equation of a circle tangent to the x-axis with center (–5, 7). Radius is 7, since center is 7 units away from x-axis. (x + 5)2 + (y ! 7)2 = 49 5. Find the equation of the line tangent to the circle at the point where the circle passes through the point (–2, 5) if the circle is centered at (1, 4). 4 ! 5 !1 = 1 ! !2 3 Perpendicular: m! = 3 Line equation: y ! 5 = 3(x + 2) Line slope would be perpendicular to radius. Radius slope: