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If omega is one of the angles between ...

If `omega` is one of the angles between the normals to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` `(b>a)` at the point whose eccentric angles are `theta` and `pi/2+theta` , then prove that `(2cotomega)/(sin2theta)=(e^2)/(sqrt(1-e^2))`

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CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the equation of the normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)...

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  2. Find the points on the ellipse (x^2)/4+(y^2)/9=1 on which the norma...

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  3. If omega is one of the angles between the normals to the ellipse (x^...

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  4. If the normal at any point P on the ellipse x^2/a^2+y^2/b^2=1 meets t...

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  5. P is the point on the ellipse isx^2/16+y^2/9=1 and Q is the correspond...

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  6. If the normal at one end of the latus rectum of the ellipse (x^2)/(...

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  7. If the normals to the ellipse x^2/a^2+y^2/b^2= 1 at the points (x1, y...

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  8. Find the normal to the ellipse (x^2)/(18)+(y^2)/8=1 at point (3, 2).

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  9. If two points are taken on the minor axis of an ellipse (x^2)/(a^2)...

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  10. If any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 intercepts e...

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  11. Find the slope of a common tangent to the ellipse (x^2)/(a^2)+(y^2)/(b...

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  12. If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^...

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  13. If F1 and F2 are the feet of the perpendiculars from the foci S1a ...

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  14. If the tangent at any point of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 m...

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  15. Two perpendicular tangents drawn to the ellipse (x^2)/(25)+(y^2)/(16)=...

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  16. A tangent having slope of -4/3 to the ellipse (x^2)/(18)+(y^2)/(32)=...

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  17. If the tangent to the ellipse x^2+2y^2=1 at point P(1/(sqrt(2)),1/2) m...

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  18. Chords of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are drawn through the...

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  19. Find the locus of the middle points of all chords of (x^2)/4+(y^2)/...

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  20. Tangents P Qa n dP R are drawn at the extremities of the chord of th...

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