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  4. A tangent to the parabola x2+4 a y=0 cuts the parabola x2=4 by at A and B. The locus of the mid point of AB has the equation :

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Q. A tangent to the parabola $x^2+4 a y=0$ cuts the parabola $x^2=4$ by at $A$ and $B$. The locus of the mid point of $AB$ has the equation :

Conic Sections

Solution:

Equation of chord $AB$ with mid point $(h, k)$ of parabola $x ^2=4$ by using $T = S _1$ $h x-2 b(y+k)=x_1{ }^2-4 b k$. It touches $x^2+4 a y=0$. Solve and put $D=0$