If $\theta$ denotes the acute angle between the curves $y=10-x^2$ and $y=2+x^2$,at a point of the intersection,then $|\tan \theta|$ is equal to

If the length of the subnormal at any point of the curve $y^n = a^{n-1}x$ is constant,then $n$ equals-

If the slope of the tangent to the curve $y=ax^3+bx+4$ at the point $(2, 14)$ is $21$, then the values of $a$ and $b$ are respectively:

The coordinates of the point$(s)$ on the graph of the function $f(x) = \frac{x^3}{3} - \frac{5x^2}{2} + 7x - 4$ where the tangent drawn cuts off intercepts from the coordinate axes which are equal in magnitude but opposite in sign,are:

If the tangent to the curve $y=x^{3}-x^{2}+x$ at the point $(a, b)$ is also tangent to the curve $y=5x^{2}+2x-25$ at the point $(2, -1)$,then $|2a+9b|$ is equal to $........$

What is the equation of the normal to the curve $y^2 = x^3$ at the point where the $x$-coordinate is $8$?