Prove that the chord `y-xsqrt(2)+4asqrt(2)=0` is a normal chord of the parabola `y^2=4a x` . Also find the point on the parabola when the given chord is normal to the parabola.

Answer

`(2a,-2sqrt(2)a)`

Explanation

Equation of normal to the parabola `y^(2)=4ax` having slope m is
`y=mx-2an-am^(3)`
Comparing this equation with `y=sqrt(2)x-4asqrt(2)`, we get `m=sqrt(2)`
`and" "2am+am^(3)=2sqrt(2)a+2sqrt(2)a=4asqrt(2)`
Thus, given on the parabola is `(am^(2),-2am)-=(2a,-2sqrt(2)a)`.