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Question

If the line x+2y+4=0 cutting the ellipse x2a2+y2b2=1 in points whose eccentric angles are 30 and 60 subtends a right angle at the origin then its equation is


A

x28+y24=1

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B

x216+y24=1

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C

x24+y216=1

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D

none of these

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Solution

The correct option is B

x216+y24=1


slope of line =ba(sin 60sin 30cos 60cos 30)=ba=12
Homogenizing the ellipse with x+2y4=0
x24b2+y2b2=(x+2y4)21b2(x24+y2)=x2+4y2+4xy16
Coefficient of x2+coefficient of y2=0
14b2116+1b2416=0b2=4,b=2a=4Ellipse is x216+y24=1


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