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Question

If the tangents drawn from a point to the parabola y2=4ax are also normals to the parabola x2=4by, then


Your Answer
A
b28a2 
Your Answer
B
b22a2 
Your Answer
C
a22b2 
Correct Answer
D
a28b2 

Solution

The correct option is D a28b2 
The equation of a tangent to y2=4ax is 
y=mx+am(1)
This is a normal to the parabola x2=4by,
So any normal to the parabola is given by 
y=mx+2b+bm2(2)
Comparing equation (1) and (2), we get
am=2b+bm22bm2am+b=0
As mR, so
D0a28b20a28b2

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