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Prove that if any tangent to the ellipse...

Prove that if any tangent to the ellipse is cut by the tangents at the endpoints of the major axis at `Ta n dT '` , then the circle whose diameter is `TT '` will pass through the foci of the ellipse.

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A DAS GUPTA-Ellipse and Hyberbola-EXERCISE
  1. A triangle has its vertices on a rectangular hyperbola. Prove that the...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. The eccentricity of a rectangular hyperbola, is

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  20. Equation of the ellipse whose focus is (6,7) directrix is x + y + 2 = ...

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