The point at which the tangent line to the curve of $y=\frac{16}{x}-x^2$ is horizontal, is

If the tangent at a point $P$ on the curve $y=4x^4+x$ is perpendicular to the tangent to the same curve at $(0,0)$,then the point $P$ is

The length of the tangent drawn at the point $P\left(\frac{\pi}{4}\right)$ on the curve $x^{\frac{2}{3}}+y^{\frac{2}{3}}=2^{\frac{2}{3}}$ is

The equation of the tangent to the curve $6y = 7 - x^3$ at the point $(1, 1)$ is:

The equation of the tangent to the curve $x y^5+2 x^2 y-x^3+y+1=0$ at $x=0$ is

If the equation of the normal to the curve $y = \frac{x-a}{(x+b)(x-2)}$ at the point $(1, -3)$ is $x - 4y = 13$,then the value of $a+b$ is equal to $.......$.