The area of the triangle formed by the co-ordinate axes and a tangent to the curve $x y=\mathrm{a}^2$ at the point $\left(x_1, y_1\right)$ is _______ sq. units (where a, $x_1$ and $y_1$ are non-zero)

The minimum value of the slope of the tangent to curve $y=x^3-3 x^2+2 x+93$ is

A spherical balloon is filled with $4500 \pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72 \pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage has begun, is

If $x$ and $y$ are sides of two squares such that $y=x-x^2$, then the rate of change of area of the second square with respect to that of the first square is