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 :

Question

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 : (A) (a+2 b) x2=4 b2 y (B) (b+2 a) x2=4 b2 y (C) (a+2 b) y2=4 b2 x (D) (b+2 x) x2=4 a2 y

Tardigrade Admin · Accepted Answer

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)=x1 2-4 b k. It touches x2+4 a y=0. Solve and put D=0

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 $A B$ has the equation :

$(a + 2 b) x^{2} = 4 b^{2} y$

$(b + 2 a) x^{2} = 4 b^{2} y$

$(a + 2 b) y^{2} = 4 b^{2} x$

$(b + 2 x) x^{2} = 4 a^{2} y$

Equation of chord $A B$ with mid point $(h, k)$ of parabola $x^{2} = 4$ by using $T = S_{1}$ $h x - 2 b (y + k) = x_{1}^{2} - 4 bk$ . It touches $x^{2} + 4 a y = 0$ . Solve and put $D = 0$

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

(a+2b)x2=4b2y

(b+2a)x2=4b2y

(a+2b)y2=4b2x

(b+2x)x2=4a2y