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Question

On the ellipse 9x2+25y2=225, then find the point the distance from which to our focus F1 is four times the distance to the other focus F2


A

-154,632

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B

-154,634

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C

-152,632

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D

(-15,63)

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Solution

The correct option is B

-154,634


Explanation for the correct option.

Finding On the ellipse 9x2+25y2=225, then find the point the distance from which to our focus F1 is four times the distance to the other focus F2

Given: Ellipse 9x2+25y2=225,
x252+y232=1a=5b=3c=a2b2c=4

as sum of distance of both focus remains same, distance from F1, of the point is 2.
[x(4)]2+y2=2(x+4)2+y2=2(4x)2+y2=4....(1)

distance from F2, of the point is 4×2=8.
(x4)2+y2=8(x+4)2+y2=64....(2)

Subtracting 2 from 1 ,We get;

(x+4)2(x4)2=6016x=60x=154

put x in (1),

41542+y2=4142+y2=4y2=4116y2=64116y=634

Hence the correct answer is option (B)


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