a variable line passes through point (h,k) find the locus of foot of perpendicular drawn to line fro

vishal batra

a variable line passes through point (h,k) find the locus of foot of perpendicular drawn to line from origin

Krishna Gopal Singh

If slope of line is m then equation of line is (y-k) = m(x-h)

For foot of perpendicular y/x = -1/m

Solving the two we get

y(1+m^2) = (k-mh)

Putting m = -x/y we get

y*(1+ x^2/y^2) = (k+ hx/y)

Or x^2 + y^2 = (ky + hx)