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If Sa n dS ' are two foci of ellipse 1...

If `Sa n dS '` are two foci of ellipse `16 x^2+25 y^2=400 and P S Q` is a focal chord such that `S P=16 ,` then find `S^(prime)Qdot`

A

`44//9`

B

`54//9`

C

`64//9`

D

`74//9`

Text Solution

Verified by Experts

The correct Answer is:
D
we have ,
`16x^(2) +25y^(2) = 400implies (x)/(25)+(y^(2))/(16)=1`
` therefore ` Semi -latusrectum `=(16)/(5)`
Now,
HM of SP and SQ = semi-latusrectum
`implies ( 2 S.P .Sq)/(SP+SQ)=(16)/(5)`
`implies (2xx16xxSQ)/(16+SQ)=(16)/(5)implies 10SQ=16+SQimplies SQ=(16)/(9)`
but ,SQ +S'Q = Major axis
`implies (16)/(9)+S'Q=10impliesS'Q-(74)/(9)`
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OBJECTIVE RD SHARMA ENGLISH-ELLIPSE-Chapter Test
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  2. Find the maximum area of an isosceles triangle inscribed in the ellip...

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  3. A tangent to the ellipse x^2+4y^2=4 meets the ellipse x^2+2y^2=6 at P&...

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  4. The distance of a point on the ellipse (x^2)/6+(y^2)/2=1 from the cent...

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  5. If the minor axis of an ellipse subtends an angle of 60^(@) at each fo...

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  6. Let Sa n dS ' be two foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . I...

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  7. The equation of the normal at the point P (2, 3) on the ellipse 9x^(2)...

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  8. For the ellipse 3x^(2) + 4y^(2) + 6x - 8y - 5 = 0 the eccentrically, i...

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  9. Let S, S' be the focil and BB' be the minor axis of the ellipse (x^(2)...

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  10. If the length of the latusrectum of the ellipse x^(2) tan^(2) theta + ...

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  11. if vertices of an ellipse are (-4,1),(6,1) and x-2y=2 is focal chord t...

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  12. If (-4, 3) and (8, 3) are the vertices of an ellipse whose eccentricit...

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  13. If the chord joining points P(alpha) and Q(beta) on the ellipse ((x^...

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  14. If P(alpha,beta) is a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1...

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  15. The tangent at any point P on the ellipse meets the tangents at the ve...

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  16. P is a point on the circle x^(2) + y^(2) = c^(2). The locus of the mid...

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  17. The equation of the locus of the poles of normal chords of the ellipse...

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  18. The locus of mid-points of focal chords of the ellipse (x^2)/(a^2)+(y^...

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  19. The locus of a point whose polar with respect to the ellipse (x^2)/(a^...

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  20. if the chord of contact of tangents from a point P to the hyperbola x...

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  21. The locus of the poles of tangents to the auxiliary circle with respec...

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