the centre of a circle is 2x - 1 3x 1find x if

Question

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