[Math] The tangent at the point $P(x_0,y_0)$ to the parabola $y^2=4ax$ meets the parabola $y^2=4a(x+b)$ at Q and R,

Question

Problem :

The tangent at the point $P(x_0,y_0)$ to the parabola $y^2=4ax$ meets the parabola $y^2=4a(x+b)$ at $Q$ and $R$, the coordinates the mid point of $QR$ are ?

Solution :

Tangent from a point $P(x_0,y_0)$ to the parabola $y^2=4ax$ is $yy_0 =2a(x+x_0)$

Request you to please suggest how to approach this problem further thanks.

Answer 1

Substitute $ y =2a(x+x_0)/y_0$ in the parabola $y^2=4a(x+b)$ then solve for x.

We will get two values for x now plug these values in the tangent equation to get y values. You will get the points.

Hope this helped.