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

Given :
Radius = 20/2 = 10 units
centre = (2x-1,3x+1)
point on circle = (-3,-1)

distance between centre and a point on circle = Radius
Distance between (2x-1,3x+1)&(-3,-1) = 10

(2x-1+3)^2 + (3x+1+1)^2 = 100
(2x+2)^2 + (3x+2)^2 = 100
4x^2+4+8x+9x^2+4+12x = 100
13x^2+20x+8 = 100
13x^2+20x-92 = 0
13x^2-26x+46x-92 = 0
13x(x-2) +46(x-2) = 0
(13x+46)(x-2) = 0
x = 2 & -2

R