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The centre of a circle is (2x - 1, 3x + 1).Find x if the circle passes through (-3,-1) and the length of the diameter is 20 units. [Ans: x = 2 , -46/13 ]
Ans : D = 20 R = 10
(2x - 1 + 3)2 + (3x + 1 + 1)2 = 102
(2x + 2)2 + (3x + 2)2 = 100
4x2 + 8x + 4 + 9x2 + 12x + 4 = 100
13x2 + 20x + 8 = 100
13x2 + 20x - 92 = 0
13x2 + 46x - 26x - 92 = 0
(13x + 46) - 2(13x + 46) = 0
x = 2, - 46/13
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