Question

Find the value of a for which the ellipse x2/a2+y2/b2=1,(a>b),if the extremities of the latus rectum of the ellipse having positive ordinates lie on the parabola x^2=-2(y-2)

Answer 1

the correct answer is "2"

Explanation:

general equation of Ellipse --> x2/a2+y2/b2=1,  a >b, for example  Major Axis Length is Twice of 2 ==> 2*a, then locus latus rectum of ellipse   is x^2 = a(a (+/-) y)

Here, the locus of  latus rectum of  ellipse have +ve dictums lie on parabola--> x² = -2(y -2) = 2(2 - y)

by comparing both equations

so,  x^2=a(a - y) and x^2 = 2(2 - y)

so, a  is 2

value of a is 2