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Question

Equation of the ellipse with focus (3,2),
eccentricity 34 and directrix 2xy+3=0 is

A
44x2+36xy+71y2374x528y+756=0
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B
44x2+36xy+71y2588x+374y+959=0
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C
44x2+36xy+71y2125x274y+659=0
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D
44x2+36xy+71y2135x47y+859=0
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Solution

The correct option is B 44x2+36xy+71y2588x+374y+959=0
Given that: Focus is (3,2), eccentricity is 34 and directrix is 2xy+3=0 Let a point on ellipse is P(x,y)
equation of ellipse is the locus of point P(x,y).
Now, equation is :
Distance of P from focus =eccentricity ×( distance of P from directrix )
(x3)2+(y+2)2=34∣ ∣ ∣2xy+322+(1)2∣ ∣ ∣
Squaring both the sides
(x3)2+(y+2)2=9162xy+352
80(x2+96x+y2+4+4y)=9(4x2+y2+94xy+12x6y)
44x2+71y2+36xy588x+374y+80×139×9=0
44x2+36xy+71y2588x+374y+959=0

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