A tangent to the parabola x 2 + 4 a y = 0 at the point T cuts the parabola x 2 = 4 b y at A \& B . Then locus of the mid point of AB is

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Let mid point of AB is M(h, k) Then equation of AB is h x − 2 b ( y + k ) = h 2 − 4 bk Let T ( 2 a t , − a t 2 ) ⇒ Equation of tangent ( AB ) = x ( 2 a t ) = − 2 a ( y − a t 2 ) Compare these two equations, we get 2 a t h ​ = 2 a − 2 b ​ = 2 a 2 t 2 h 2 − 2 bk ​ By eliminating t and Locus (h, k), we get ( a + 2 b ) x 2 = 4 b 2 y

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