Question

Write the coordinates of the centre of the circle passing through (0, 0), (4, 0) and (0, -6).

Answer 1

Circle is passing through A(0, 0), B(4, 0) and (0, -6)
Let equation of circle be,
$(x-h{)}^2+(y-k{)}^2=r^2\dots \left(i\right)$
circle (1) is passing through
$A(0,0)(0-h{)}^2+(0-k{)}^2=r^2{h}^2+k^2=r^2\dots \left(2\right)$
circle (1) is passing through B(4, 0)
$(4-h{)}^2+(0-k{)}^2=r^2(4-h{)}^2+k^2=r^2\dots (3)$
circle (1) is passing through B(0, -6)
$(0-h{)}^2+(-6-k{)}^2=r^2{h}^2+(6+k^2)=r^2\dots \left(4\right)\left[\right(2)-(3\left)\right],h^2-(4-h{)}^2=0(h-4+h\left)\right(h+4-h)=0(2h-4\left)\right(4)=0h=2[\left(2\right)-\left(4\right)],k^2-(6+k{)}^2=0(k-4-k)(k+6+k)=0(-6)(2k+6)=0k=-3$
Put the value of h and k in equation (1)
$h^2+k^2=r^2(2{)}^2+(-3{)}^2=r2r^2=13$
Centre of the circle =(2, -3)