Two circles are drawn through the points (a,5a) and (4a,a) to touch the axis of y. Find the angle at which they intersect.

letx^2 + y^2 + 2gx + 2fy + c = 0 be the eqn of circle which has 3 variables g,f, and c.

now if passes thruthe points (a,5a) and (4a,a) so they will satisfy in the eqn

hence we get 2 eqns

also it touches y axis hence f^2 – c = 0 ------(3)

Now solve eqn 1, 2 and 3 and find the circles and hence find angle between them

Thanks

Approved