Question

Find the locus of middle point of the chord of the parabola $y^2=4ax$ whose slope is 'm'

Answer 1

Let P(h, k) be the mid point of chord of parabola $y^2=4ax$
so equation of chord is yk - 2a (x + h) = $k^2-4ah$
but slope = $=\frac{2a}{k}=m$ $\therefore$ locus is $y=\frac{2a}{m}$