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Let P be a point on the ellipse Let the ...

Let P be a point on the ellipse Let the line parallel to y-axis passing through P meet the circle `x^(2) + y^(2) = a^(2)` at the point Q such that P and Q are on the same side of x - axis. For two positive real numbers r and s, show that the locus of R on PQ such that PQ : RQ = r : s as P varies over the ellipse is an ellipse.

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AAKASH SERIES-ELLIPSE-ADDITIONAL EXERCISE
  1. The tangent at a point P(theta) to the ellipse x^2/a^2+y^2/b^2=1 cuts ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Find the shortest distance between the ellipse x^(2) + 2y^(2) = 2 and ...

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  16. Given the base of the triangle and the sum of tangent of base angles a...

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  17. If a circle intercepts the ellipse at four points, show that the sum o...

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  18. If a line is drawn through a point A(3,4) to cut the circle x^(2)+y^(2...

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  19. From a variable point P tangents are drawn to the ellipse 4x^(2) + 9y^...

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  20. Tangents are drawn to the ellipse (x^(2))/(a^(2)) +(y^(2))/( b^(2)) =a...

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