91Ó°ÊÓ

The area bounded by the curves \(y=-\sqrt{-x}\) and \(x=-\sqrt{-y}\) where \(x, y \leq 0\) (a) cannot be determined (b) is \(1 / 3\) (c) is \(2 / 3\) (d) is same as that of the figure bounded by the curves \(y=\sqrt{-x} ; x \leq 0\) and \(x=\sqrt{-y} ; y \leq 0\)

The area enclosed by the asteroid \(\left(\frac{x}{a}\right)^{2 / 3}+\left(\frac{y}{a}\right)^{2 / 3}=1\) is (a) \(\frac{3}{4} a^{2} \pi\) (b) \(\frac{3}{18} \pi a^{2}\) (c) \(\frac{3}{8} \pi a^{2}\) (d) \(\frac{3}{4} a \pi\)

Find the maximum area of the ellipse that can be inscribed in an isosceles triangles of area \(A\) and having one axis lying along the perpendicular from the vertex of the triangles to its base.