Two thin rods AB and CD of length 2a and 2b moves along OX and OY where O is the origin. Find the locus of the center of the circle passing through the extremities of the two rods.
My attempt:-
There are two points (2a,0) and (0,2b) through which the circle passes, So let the center C be (h,k) and radius r
$(h-2a)^2 + k^2 = r^2$
$h^2 + (k-2b)^2 = r^2$
$(h-2a)^2 + k^2 = h^2 + (k-2b)^2$
$-4ax+4a^2 = -4bk + 4b^2$
$a^2-b^2 = ax-bk$ I don't know what to do next.
The correct answer is $x^2-y^2 = a^2-b^2$