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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 :
Hello student,The given ellipse is b2x2 + y2 = a2b2i.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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