54. The centre of a circle is (2x- 1,3x + 1) and radius is 10 i.Find t

1.	54. The centre of a circle is (2x- 1,3x + 1) and radius is 10 i.Find the value of xnasses through the noint (-1
Answer» Given diameter of the circle = 20 units Radius of the circle = d/2 = 20/2 = 10 units Given center of a circle is (2x - 1, 3x + 1) Given that circle passes through (-3, -1), So, distance of (-3, -1) from the center of the circle should be equal to radius of the circle Hence, √(2x + 2)² + (3x + 2)² = 10 Squaring on both sides, we get (2x + 2)² + (3x + 2)² = 100 13x² + 20x - 92 = 0 13x² -26x + 46x -92 = 0 13x(x - 2) + 46(x - 2) = 0 (13x + 46)(x - 2) = 0 Hence, x = 2 or -46/13 the diameter of the circle =20 units

54. The centre of a circle is (2x- 1,3x + 1) and radius is 10 i.Find the value of xnasses through the noint (-1

Answer»

Given diameter of the circle = 20 units

Radius of the circle = d/2 = 20/2 = 10 units

Given center of a circle is (2x - 1, 3x + 1)

Given that circle passes through (-3, -1),

So, distance of (-3, -1) from the center of the circle should be equal to radius

of the circle

Hence, √(2x + 2)² + (3x + 2)² = 10

Squaring on both sides, we get

(2x + 2)² + (3x + 2)² = 100

13x² + 20x - 92 = 0

13x² -26x + 46x -92 = 0

13x(x - 2) + 46(x - 2) = 0

(13x + 46)(x - 2) = 0

Hence, x = 2 or -46/13

the diameter of the circle =20 units