The locus of the extrimities of the latusrectum of the family of ellipses b^2 x^2+y^2=a^2 b^2 having a given major axis, is

Step-by-step solution

Given equation is b^2 x^2+y^2=a^2 b^2 x^2 a^2 + y^2 a^2 b^2 =1 ....(i) Above equation of an ellipse with semi-major axis (a) and semi-minor axis (ab). N̦ow, ecentricity, e=1- a^2 b^2 a^2 b^2=1-e^2 ....(ii) Let (x, y) be extrimities of latusrectum, then aligned x & =a e and y= a^2 b^2 a x a & =e and y a = b^2 aligned From Eq. (ii), we get y a =1- x^2 a^2 a y+x^2=a^2 Hence, locus of latusrectum is x^2 a y=a^2 .