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Tangents to the ellipse x^(2)//a^(2)+y^(...

Tangents to the ellipse `x^(2)//a^(2)+y^(2)//b^(2)=1` make angles `theta_(1), theta_(2)` with the major axis. The equation of the locus of their point of intersection when `tan(theta_(1)+theta_(2))=k` is

A

`xy=k(x^(2)+y^(2)+a^(2)+b^(2))`

B

`2xy=k(x^(2)-y^(2)+a^(2)+b^(2))`

C

`2xy=k(x^(2)-y^(2)-a^(2)+b^(2))`

D

`2xy=k(x^(2)-y^(2)-a^(2)-b^(2))`

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DIPTI PUBLICATION ( AP EAMET)-ELLIPSE-EXERCISE 1A
  1. The sum of the squares of the perpendiculars on any tangent to the ell...

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  2. Let d and d^(') be the perpendicular distances from the foci of an ell...

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  3. Tangents to the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 make angles theta(...

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  4. The tangent to x^(2)//a^(2)+y^(2)//b^(2)=1 meets the major and minor a...

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  5. S (3, 4) and S^(') (9, 12) are the focii of an ellipse and the foot of...

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  6. The locus of the foot of the perpendicular drawn from the centre of th...

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  7. The area (in sq . Unit ) of the quadrilateral formed by the tangents a...

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  8. C is the centre of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 and...

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  9. If the normal at the end of latus rectum of an ellipse x^(2)//a^(2)+y^...

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  10. The slope of a common tangent to the ellipse x^(2)//a^(2)+y^(2)//b^(2)...

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  11. The parametric representation (2+t^(2),2t+1) represents

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  12. The points on the ellipse 2x^(2)+3y^(2)=6 whose eccentric angles diffe...

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  13. The equation of the tangent at a point theta=3pi//4 to the ellipse x^(...

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  14. The equation of the normal to the ellipse x^(2)//16+y^(2)//9=1 at the...

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  15. If x/a+y/b=sqrt(2) touches the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1, then...

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

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  17. The eccentric angles of the extremities of latusrecta of the ellipse x...

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  18. The tangent and normal to the ellipse 4x^(2)+9y^(2)=36 at a point P on...

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  19. If alpha and beta are the eccentric angles of the ends of a focal chor...

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  20. The tangent at a point P(acos theta,bsin theta) on the ellipse (x^(2))...

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