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Question

The eccentricity of an ellipse with center at the origin is 12 if one of its directrices is x=-4, then the equation of the normal to it at (1,32) is

A
2y-x=2
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B
4x-2y=1
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C
4x+2y=7
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D
x+2y=4
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Solution

The correct option is B 4x-2y=1
We have e=12 and ae=4a=2
Now b2=a2(1e2)=(2)2[1(12)2]=4(114)=3b=3
Equation of the ellipse is x2(2)2+y2(3)2=1x24+y23=1
Now the equation of normal at (1,32)isa2xx1b2yy1=a2b2
4x13y32=434x2y=1

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