Quiz14solutions - MAC1105: Quiz #14 Solutions July 21, 2010...

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Unformatted text preview: MAC1105: Quiz #14 Solutions July 21, 2010 In the top-right corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. 1. Determine which of the following points is on the graph of y 2 - x3 = 1: (-1,-2); (1,0); (3,2); (3,-2); (0,-1) 2. Consider the points A = (3, 7) and B = (-9, 1) (a) Find the distance between A and B (Hint: 180 = 36 5). 2 2 d(A, B) = (x2 - x1 ) + (y2 - y1 ) = 180 = 36 5 = 6 5 (-9 - 3)2 + (7 - 1)2 = 144 + 36 = (b) Find the midpoint of the line segment AB . x1 + x2 y1 + y2 , 2 2 = -9+3 7+1 2 , 2 = (-3, 4). 3. Write the following equation for a circle in standard form, and state its center and radius: x2 + y 2 + 4x - 8y + 4 = 0 We need to complete the square twice. So we set up: x2 + 4x + ( ) + y 2 - 8y + ( ) = -4 + ( ) + ( ) ( 4 )2 = 4 and ( -8 )2 = 16, so we have 2 2 x2 + 4x + 4 + y 2 - 8y + 16 = -4 + 4 + 16 (x + 2)2 + (y - 4)2 = 16 So the center is (-2, 4) and the radius is 4. 1 ...
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