Question

Middle point of the chord of the parabola $y^2=4ax$ which pass through a given point (p, q)

Answer 1

Let P(h, k) be the mid point of chord of parabola $y^2=4ax$
so equation of chord is $yk-2a(x+h)=k^2-4ah$ Since it passes through $(p,q)$
$\therefore qk-2a(p+h)=k^2-4ah$ $\therefore$ Required locus is $y^2-2ax-qy+2ap=0$