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Prove that the product of the perpendicu...

Prove that the product of the perpendicular from the foci on any tangent to an ellipse is equal to the square of the semi-minor axis.

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A DAS GUPTA-Ellipse and Hyberbola-EXERCISE
  1. P N is the ordinate of any point P on the hyperbola (x^2)/(a^2)-(y^2)/...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. A circle with centre (3alpha, 3beta) and of variable radius cuts the ...

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  16. The locus of the point of intersection of the tangents at the end-poin...

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  17. Find the locus of the-mid points of the chords of the circle x^2 + y^2...

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  18. If alpha and beta be the angles subtended by the major axis to an elli...

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  19. The equation x^2-3xy+y^2+10x-10y+21=0represents a having its centre at...

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  20. The eccentricity of a rectangular hyperbola, is

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