Analytical Geometry: 2D and 3D by P. R. Vittal

Author:P. R. Vittal [Vittal, P. R.]
Language: eng
Format: epub
ISBN: 9789332517646
Google: QlmFAQAACAAJ
Publisher: Dorling Kindersley (India)
Published: 2013-01-15T10:41:35+00:00

Let P and D be the extremities of a pair of conjugate diameters of the ellipse (7.129). Let P and D be the points P(a cosθ, b sinθ) and D(−a sinθ, b cosθ). The equations of the normal at P and D are

Solving equations (7.130) and (7.131), we get,

Squaring and adding, we get

Therefore, the locus of the point of intersection of these two normals is (a2x2 + b2y2)3 = (a2 − b2)2 (a2x2 − b2y2)2.

Example 7.63

If the point of intersection of the ellipses and be at the extremities of the conjugate diameters of the former then prove that

Solution

The given ellipses are

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