If $A=\left[\begin{array}{ll}4 & 5 \\ 2 & 1\end{array}\right]$ and $A^2-5 A-6 I=0$, then $A^{-1}=$

The quadratic equation whose roots are the numbers having arithmetic mean 34 and geometric mean 16 is

If $x=a \sin t-b \cos t, y=a \cos t+b \sin t$, then $y^3 \frac{d^2 y}{d x^2}+x^2+y^2=$

The area of the triangle formed by the lines joining vertex of the parabola $x^2=12 y$ to the extremities of its latus rectum is