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Question

If a normal of slope m to the parabola y2=4ax touches the hyperbola x2−y2=a2, then

A
m64m43m2+1=0
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B
m64m4+3m21=0
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C
m6+4m43m2+1=0
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D
m6+4m4+3m2+1=0
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Solution

The correct option is D m6+4m4+3m2+1=0
Equation of normal with slope m to the parabola y2=4ax is given by,
y=mx2amam3
Also this line touches the hyperbola x2y2=a2
thus using condition of tangency to the hyperbola, c2=a2m2b2
(2amam3)2=a2(m21)
4m2+m6+4m4=m21
m6+4m4+3m2+1=0
Hence, option 'D' is correct.

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