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PQ is a chord of the ellipse through the...

PQ is a chord of the ellipse through the centre. If the square of its length is the harmonic mean ofthe squares of lengths major and minor axes then its inclination with the major axis is

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A DAS GUPTA-Ellipse and Hyberbola-EXERCISE
  1. Find the latus rectum, eccentricity and foci of the curve 4x^(2)+9y^(2...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. A variable straight line of slope 4 intersects the hyperbola xy=1 at t...

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  18. Prove that the locus of the middle-points of the chords of the hyperbo...

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  19. A normal to the hyperbola x^2-4y^2=4 meets the x and y axes at A and B...

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  20. A circle cuts two perpendicular lines so that each intercept is of giv...

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