Question

The centre of a circle is (2x - 1, 3x + 1). Find x if the circle passes through (-3, -1) and the length of its diameter is 20 unit.

Answer 1

Distance between the points A (2x - 1, 3x + 1) and B (- 3, - 1) = Radius of circle
AB = 10 (Since, diameter = 20 units, given)
AB² = 100
(-3 - 2x + 1)² + (-1 - 3x - 1)² = 100

(-2 - 2x)² + (-2 - 3x)² = 100

4 + 4x² + 8x + 4 + 9x² + 12x = 100

13x² + 20x - 92 = 0

x = `(-20 ± sqrt(400 + 4784))/(26)`

x = `(-20 ± 72)/(26)`

x = 2, - `(46)/(13)`.