The abscissae of the points,where the tangent to the curve $y=x^{3}-3x^{2}-9x+5$ is parallel to the $x$-axis,are

If the lines $x+y=a$ and $x-y=b$ touch the curve $y = x^{2}-3x+2$ at the points where the curve intersects the $x$-axis,then $\frac{a}{b}$ is equal to:

If the curves $x=y^{4}$ and $xy=k$ cut at right angles,then $(4k)^{6}$ is equal to ..... .

If $P$ and $Q$ are two different points on the curve $y = x^3 - x$ such that the tangent at $P$ intersects the curve again at $Q$,then $\frac{m_{OQ} + 1}{m_{OP} + 1}$ is equal to,where $O$ is the origin and $m_{AB}$ represents the slope of the line segment $AB$.

The angle between the curves $y^2=4x+4$ and $y^2=36(9-x)$ is (in $^{\circ}$)

The coordinates of a point on the curve $y = x \log x$ at which the normal is parallel to the line $2x - 2y = 3$ are