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An ellipse has eccentricity 1/2 and one...

An ellipse has eccentricity `1/2` and one focus at the point `P(1/2,1)`. Its one directrix is the comionand tangent nearer to the point the P to the hyperbolaof `x^2-y^2=1` and the circle `x^2+y^2=1`.Find the equation of the ellipse.

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A DAS GUPTA-Ellipse and Hyberbola-EXERCISE
  1. An ellipse has eccentricity 1/2 and one focus at the point P(1/2,1)....

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  2. Find the equation to the ellipse whose one vertex is (3,1), the nearer...

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  3. Find the equation of the ellipse whose centre is (-2,3) and whose semi...

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  4. Find the equation of the hyperbola whose foci are (6,4)a n d(-4,4) and...

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  5. If e and e\' are the eccentricities of the hyperbola x^2/a^2 - y^2/b^2...

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  6. Find the latus rectum, eccentricity and foci of the curve 4x^(2)+9y^(2...

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  7. Find the centre, eccentricity, foci and directrices of the hyperbola :...

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  8. PQ is a chord of the ellipse through the centre. If the square of its ...

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  9. Length of the focal chord of the ellipse x^2/a^2+y^2/b^2= 1 which is ...

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  10. If alpha and beta are eccentric angles of the ends of a focal chord of...

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  11. The hyperbola x^2/a^2 - y^2/a^2 - y^2/b^2 = 1 passes through the point...

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  12. P N is the ordinate of any point P on the hyperbola (x^2)/(a^2)-(y^2)/...

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  13. A triangle has its vertices on a rectangular hyperbola. Prove that the...

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  14. Prove that the product of the perpendicular from the foci on any tange...

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  15. Prove that if any tangent to the ellipse is cut by the tangents at the...

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

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  17. Find the equations of the tangents from the point (2,2) to the ellipse...

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  18. If the normal at an end of a latus rectaum of an ellipse passes thr...

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  19. The locus of the point of intersection of tangents to the ellipse x^(2...

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  20. If the normal at any point P on the ellipse cuts the major and mirror ...

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  21. Find the locus of the foot of the perpendicular drawn from the cent...

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