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## Homework Statement

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If the tangent at the point ##P## to the parabola ## y^2=4ax## meets the parabola ## y^2=4a(x+b)## at points ##Q## and ##R##. Prove that ##P## is the midpoint of ##QR##

## Homework Equations

## The Attempt at a Solution

We know that the tangent equation to the parabola ## y^2=4ax## is given by ##yy1=2a(x+x1)##

and that ## y^2=4a(x+b)## it follows that

##2a(x+x1) = 4a(x+b)##

→## (x+x1)=2(x+b)##

→##P= 2QR##

or

→##1/2P=QR##

is my working correct?

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