- #1

utkarshakash

Gold Member

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## Homework Statement

Three normals are drawn from the point (14,7) to the curve [itex]\large y^{2} -16x-8y=0[/itex]. Find the co-ordinates of the feet of the normals.

## Homework Equations

Converting the equation of parabola in the form of a perfect square I get

[itex]\large (y-4)^{2}=16(x+1)[/itex]

## The Attempt at a Solution

I know that for the parabola [itex]\large y^{2}=4ax[/itex] the equation of normal is [itex]\large y=-tx+2at+at^{3}[/itex]. But what will be the equation of normal for the parabola in this question? If I get to know the equation of normal in terms of t then I can get a cubic equation in t and by solving that equation I can obtain the coordinates of feet of normals. But I'm falling short of the equation of normal. How do I get it?