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Prove that the sum of the squares of the...

Prove that the sum of the squares of the perpendiculars on any tangent of the ellipse form the points on the minor axis is `2a^(2)`

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AAKASH SERIES-ELLIPSE-ADDITIONAL EXERCISE
  1. Show that the locus of middle points of a focal chord of an ellipe (x^...

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  2. The locus of mid points of the chords of the ellipse (x^(2))/(a^(2))+...

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  3. Prove that the sum of the squares of the perpendiculars on any tangent...

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  4. Find the locus of point of intersection of tangents to the ellipse x^2...

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  5. P and P' are corresponding points on an ellipse and its auxilliary cir...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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