Two rods of length a and b, slide along the axes which are rectangular, in such a manner that their ends are always con-cyclic. The locus of the cente of the circle passing through these ends is ?
Locus of centre of circle.
let the center of the circle be (h,k)
assuming rod of length a slides along y-axis and other slides along x-axis.
then for the rod of length a -
length of perpendicular from center = h
radius of circle = r
and length of chord = a
then (a/2)2 + h2 = r2
similarly for other rod
(b/2)2 + k2 = r2
so the locus of the center is (a/2)2 + x2= (b/2)2 + y2