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PQ and PR are two focal chords of the el...

PQ and PR are two focal chords of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`, if `2 alpha, 2 beta and 2 gamma` are the eccentric angles of the point P,.Q and R respectively, prove that, `cot alpha cot beta = tan gamma tan beta`.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. If two distinct chords, drawn from the point (p,q) on the circle x^(2)...

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  2. A variable line L passing through the point B(2,5) intesects the lines...

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  3. For all values of a and, b show that the circle (x-2)(x-2+a)+(y+3) (y+...

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  4. A circle C(1) of diameter 6 units, is in the first quadrant and it tou...

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  5. Find he point on the straight line y=2x+11 which is nearest to the cir...

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  6. On the parabola y^(2)=4ax, P is the point with parameter t,Q is the op...

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  7. Through the vertex A of a parabola the chords AP and AQ are drawn at ...

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  8. Show that the sum of the ordinate of end of any chord of a system of p...

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  9. An equilateral triangle is inscribed within the parabola y^(2)=4ax wit...

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  10. P,Q and R three points on the parabola y^(2)=4ax. If Pq passes through...

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  11. A line of length (a+b) unit moves in such a way that its ends are alwa...

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  12. show that the length of the focal chord of the ellipse (x^(2))/(a^(2))...

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  13. A rod of given length (a+b) unit moves so that its ends are always on ...

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  14. If theta and phi be the eccentric angles of the extremities of a focal...

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  15. theta and phi are the eccentric angles of two points on an ellipse who...

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  16. PQ and PR are two focal chords of the ellipse (x^(2))/(a^(2))+(y^(2))/...

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  17. Find the locus of middle points of chords of the ellipse (x^(2))/(a^(2...

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  18. Find the length of chord of the ellipse (x^(2))/(25)+(y^(2))/(16)=1, ...

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  19. An ellipse has OB as a semi-minor axis, F and F' are its two foci and ...

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  20. Let P b any point on the hyperbola(x^(2))/(a^(2))-(y^(2))/(b^(2))=1 w...

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