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Question

The eccentricity of an ellipse whose centre is 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
2yx=2
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B
4x2y=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 4x2y=1
As directrix is parallel to yaxis hence ellipse will be standard horizontal ellipse.
Eccentricity, e=12
Let 2a and 2b be the length of the major-axis and minor-axis respectively.
ae=4a=2
e=121b2a2=12
b=3
Equation of ellipse is x24+y23=1

Thus, equation of normal at (1,32) is
4x13y3/2=1
4x2y=1

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