The centre of the circle is (2x - 1, 3x + 1) and radius is 10 units. Find the value of x if the circle passes through the point (- 3, - 1).

Given that the circle has centre O(2x - 1, 3x + 1) and passes through the point A(- 3, - 1) and has a radius(r) of 10 units.

We know that the radius of the circle is the distance between the centre and any point on the circle.

So, we have r = OA

⇒ OA = 10

⇒ OA² = 100

⇒ (2x - 1 - (- 3))² + (3x + 1 - (- 1))² = 100

⇒ (2x + 2)² + (3x + 2)² = 100

⇒ 4x² + 8x + 4 + 9x² + 12x + 4 = 100

⇒ 13x² + 20x - 92 = 0

⇒ 13x² - 26x + 46x - 92 = 0

⇒ 13x(x - 2) + 46(x - 2) = 0

⇒ (13x + 46)(x - 2) = 0

⇒ 13x + 46 = 0 (or) x - 2 = 0

⇒ 13x = - 46 (or) x = 2

∴ The values of the x are or 2.