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The tangent at a point P(acos theta,bsin...

The tangent at a point `P(acos theta,bsin theta)` on the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` meets the auxillary circle in two points. The chord joining them subtends a right angle at the centre. Find the eccentricity of the ellipse:

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The correct Answer is:
`(sin alpha+beta)/(sin (alpha+beta))`
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AAKASH SERIES-ELLIPSE-ADDITIONAL EXERCISE
  1. P and P' are corresponding points on an ellipse and its auxilliary cir...

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  2. If any tangent to the ellipse makes intercepts of lengths p and q on ...

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  3. The tangent at a point P(acos theta,bsin theta) on the ellipse (x^(2))...

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  4. Find the area of the triangle formed by three points on the ellipse x^...

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  5. If the normal at any point P on the ellipse meets the axes in G and g ...

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  6. Show that the area of a triangle inscribed in an ellipse bears a const...

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  7. The tangent at a point P(theta) to the ellipse x^2/a^2+y^2/b^2=1 cuts ...

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  8. If foci and the ends of the minor axis of an ellipse are the vertices ...

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  9. Prove that the locus of an end of latusrectum of all ellipses having a...

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  10. Show that the length of common tangent to the ellipse 'x^(2)/(25)+y^(2...

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  11. Let d be the perpendicular distance from the centre of the ellipse x^(...

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  12. Find the point on the curve 4x^(2) + a^(2)y^(2) = 4a^(2), 4lta^(2)lt8,...

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  13. Prove that in an ellipse the perpendicular from focus upon any tangent...

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  14. Let P be a point on the ellipse Let the line parallel to y-axis passin...

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  15. Let P be a point on the ellipse Let the line parallel to y-axis passin...

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  16. Consider the family of circles If in the 1st quadrant, the common tang...

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  17. Show that the maximum distance of centre of the ellipse x^(2)/a^(2)+y^...

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  18. The product of the perpendiculars from the foci on any tangent to the...

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  19. Prove that the locus of mid points of the chords (x^(2))/(a^(2))+(y^(2...

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  20. Prove that the locus of mid points of the chords (x^(2))/(a^(2))+(y^(2...

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