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Question

The normals to the parabola y2=4ax from the point (5a,2a) are

A
y=3x+33a
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B
x=3y+3a
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C
y=x3a
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D
y=2x+12a
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Solution

The correct options are
C y=2x+12a
D y=x3a
Equation of normal at point t to the parabola y2=4ax is given by
y+tx=2at+at3
Given it passes through (5a,2a)
2a+5at=2at+at3t33t2=0(t+1)2(t2)=0t=1,2
Hence required normals are
y=x3a,y=2x+12a

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