Question

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

Answer 1

$r=10,(x,y)=(-3,1)$

$=(h,k)=(2x-1,3x+1)$

$(x-h{)}^2+(y-k{)}^2=r^2$

$(-3-2x+1{)}^2+(1-3x-1)=100$

$(-2-2x{)}^2+(1-3x{)}^2=100$

$13x^2+4x-96=0$

root = $\frac{-4\pm \sqrt{4^2+4\times 36\times 13}}{2\times 13}$

$=\frac{-4\pm 70.76}{2\times 13}$

$x=2.90,-3.25$