If the curve $y=ax^2-6x+b$ passes through $(0,4)$ and has its tangent parallel to the $x$-axis at $x=\frac{3}{2}$,then the values of $a$ and $b$ respectively are

Find the equation of the normal to the curve $y=x^3-3x$ which is parallel to the line $2x+18y=9$.

$A$ curve is represented by the equations $x = \sec^2 t$ and $y = \cot t$,where $t$ is a parameter. If the tangent at the point $P$ on the curve where $t = \pi/4$ meets the curve again at the point $Q$,then the $x$-coordinate of $Q$ is equal to

If the slope of the tangent to the curve $y = x^3$ at a point is equal to the $y$-coordinate of that point,then the point is:

Find the equation of the tangent to the curve $y = be^{-x/a}$ at the point where it crosses the $y$-axis.

The chord of the curve $y=x^{2}+2ax+b$ joining the points where $x=\alpha$ and $x=\beta$ is parallel to the tangent to the curve at abscissa $x$ equal to: