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

Answer: a = 2

Step-by-step explanation:

Concept : if standard equation of ellipse is x²/a² + y²/b² = 1 , where a ≥ b, e.g., length of major axis is 2a then locus of extremities of the latusrectum of given ellipse  x² = a(a ± y)

Here, the extremities of the latusrectum of the ellipse having positive ordinaries lie on the parabola x² = -2(y -2) = 2(2 - y)

Compare both the given equations ,

e.g., x² =a(a - y) and x² = 2(2 - y)

So, a = 2

Hence, value of a = 2