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The locus of the extremities of the latus rectum of the family of ellipses b 2 x 2 +y 2 =a 2 b 2 having a given major axes is :

The locus of the extremities of the latus rectum of the family of ellipses b2x2+y2=a2b2 having a given major axes is :

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1 Answers

Latika Leekha
askIITians Faculty 165 Points
8 years ago
Hello student,
The given ellipse is b2x2 + y2 = a2b2
i.e. x2/a2 + y2/b2 = 1.
(ab)2 = a2(1 – e2) or b2 = 1 - e2.
Let an extremity of latus rectum be L(x, y).
Then, x = ae gives x2 = a2e2 = a2(1 – b2) .... (a)
and y = (ab)2/a = ab2 .... (b)
From (a) and (b) we have x2 = a2 – a(ab2)
Hence, locus of L or L’ = x2 =a2 ± ay.

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