The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is

If the curves $y^2=6 x$ and $9 x^2+b y^2=16$ intersect each other at right angles, then the value of $b$ is

The position of a point in time $t$ is given by $x=\mathrm{a}+\mathrm{bt}-\mathrm{ct}^2, y=\mathrm{at}+\mathrm{bt}^2$. It's resultant acceleration at time $t$ in seconds is given by

The equation of tangent to the curve $y=\cos (x+y)$ where $-2 \pi \leq x \leq 2 \pi$ and which is parallel to the line $x+2 y=0$, is