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

If the tangent to the curve $xy+ax+by=0$ at $(1,1)$ makes an angle $\tan^{-1} 2$ with the $x$-axis, then $\frac{a+b}{ab} =$

The area of the triangle formed by the tangent and the normal drawn to the curve $y^2=4x$ at $(1,2)$ with the $Y$-axis is (in square units):

The curve $\left(\frac{x}{a}\right)^n+\left(\frac{y}{b}\right)^n=2$,where $n \in N$,touches the line at the point $(a, b)$. Find the equation of the line.

If the line $x + By + C = 0$ is the normal to the curve given by $x = a \sin^3 t$ and $y = b \cos^3 t$ (where $a, b \neq 0$) at the point $t = \frac{\pi}{2}$, then $B - C =$

If the line $ax + by + c = 0$ is a tangent to the curve $xy = 4$,then which of the following is true regarding the signs of $a$ and $b$?