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 units.


please give the step by step explanation. It is very urgent and please don't write anything and everything to earn points.​

Answer 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 ⇒ x = -46/13 (or) x = 2 ∴ The values of the x are -46/13 or 2

Answer 2

Answer:

x=2.90,−3.25

Step-by-step explanation:

r=10,(x,y)=(−3,1)

=(h,k)=(2x−1,3x+1)

(x−h)^2 +(y−k) ^2

=r^2

(−3−2x+1)^2 + (1−3x−1)=100

(−2−2x) ^2 + (1−3x) ^2

=100

13x^2+4x−96=0

__________

root = 4±√4^2+4×36×13 / 2×13

=4+70.76/2×13

x=2.90,−3.25