# Find the locus of middle point of the chord of the parabola $$y^2$$ = 4ax which pass through a given (p, q).

## Solution :

Let P(h,k) be the mid point of chord of the 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

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