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 tothe parabola.

Prove that the chord `y-xsqrt(2)+4asqrt(2)=0`is a normal chord of the

1.	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 tothe parabola.
Answer» Correct Answer - `(2a,-2sqrt(2)a)` 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)`.

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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 tothe parabola.

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