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Find the equations of normal to the para...

Find the equations of normal to the parabola `y^2=4a x` at the ends of the latus rectum.

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End point of latus rectum of parabola `y^(2)=4ax` are P(a,2a) and Q(a-2a).
Comparing with `(at^(2),2at)` , we get t=1 for point P and t=-1 for point Q.
Now, equation of normal at point `(at^(2),2at)` is y=-tx+2at+ `at^(3)`
So, equation of normal at point P is y=-x+2a+a or x+y=3a.
Also, equation of normal at point Q is y=x-2a-a or x-y=3a.
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