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Question

Equation of the ellipse with focus (3,2), eccentricity 14 and directrix 2xy+3=0 is :

A
76x2+79y24xy492x326y1031=0
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B
76x2+79y2+4xy492x+326y+1031=0
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C
44x2+36xy+71y2125x274y+659=0
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D
44x2+36xy+71y2135x47xy+859=0
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Solution

The correct option is D 76x2+79y2+4xy492x+326y+1031=0
Focus S(3,2)
e=14
Equation of directrix is 2xy+3=0
Let P(x,y) be a point on the ellipse.
Since, for an ellipse
PS2=e2PM2
(x3)2+(y+2)2=116(2xy+3)25
76x2+79y2+4xy492x+326y+1031=0

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