If the area (in $sq. units$) of the region $\{(x,y): y^2 \le 4x, x + y \le 1, x \ge 0, y \ge 0\}$ is $a\sqrt{2} + b$,then $a - b$ is equal to

The area of the region common to the parabolas $4y^2 = 9x$ and $3x^2 = 16y$ is...

The area of the region $\{(x, y): x^2 \leq y \leq 8-x^2, y \leq 7\}$ is

The area bounded by the curves $y=(x-1)^2$,$y=(x+1)^2$ and $y=\frac{1}{4}$ is

The area (in sq. units) of the region bounded by the curves $y = x \log x$ and $y = 2x - 2x^2$ is

Let $C_{1}$ be the curve obtained by the solution of the differential equation $2xy \frac{dy}{dx} = y^{2} - x^{2}, x > 0$. Let the curve $C_{2}$ be the solution of $\frac{2xy}{x^{2} - y^{2}} = \frac{dy}{dx}$. If both the curves pass through $(1, 1)$,then the area enclosed by the curves $C_{1}$ and $C_{2}$ is equal to: