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A circle has the same center as an ellip...

A circle has the same center as an ellipse and passes through the foci `F_1a n dF_2` of the ellipse, such that the two cuves intersect at four points. Let `P` be any one of their point of intersection. If the major axis of the ellipse is 17 and the area of triangle `P F_1F_2` is 30, then the distance between the foci is 13 (b) 10 (c) 11 (d) none of these

A

12

B

13

C

14

D

15

Text Solution

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The correct Answer is:
C, D
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A circle has the same center as an ellipse and passes through the foci F_1a n dF_2 of the ellipse, such that the two cuves intersect at four points. Let P be any one of their point of intersection. If the major axis of the ellipse is 17 and the area of triangle P F_1F_2 is 30, then the distance between the foci is (a)13 (b) 10 (c) 11 (d) none of these

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Knowledge Check

  • The ellipse 4x^(2) + 9y^(2) = 36 and the hyperbola 4x^(2) – y^(2) = 4 have the same foci and they intersect at right angles then the equation of the circle through the points of intersection of two conics is

    A
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    B
    `sqrt5(x^(2)+y^(2))-3x-4y=0`
    C
    `sqrt5(x^(2)+y^(2))+3x+4y=0`
    D
    `x^(2) + y^(2) = 25`

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