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Question

# Equation of the ellipse with focus (3,âˆ’2), eccentricity 34 and directrix 2xâˆ’y+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+71y2−588x+374y+959=0Given that: Focus is (3,−2), eccentricity is 34 and directrix is 2x−y+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 ) ⇒√(x−3)2+(y+2)2=34∣∣ ∣ ∣∣2x−y+3√22+(−1)2∣∣ ∣ ∣∣ Squaring both the sides ⇒(x−3)2+(y+2)2=916∣∣∣2x−y+3√5∣∣∣2 ⇒80(x2+9−6x+y2+4+4y)=9(4x2+y2+9−4xy+12x−6y) ⇒44x2+71y2+36xy−588x+374y+80×13−9×9=0 ⇒44x2+36xy+71y2−588x+374y+959=0

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