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

The normal to the curve $x = 9(1 + \cos \theta)$,$y = 9 \sin \theta$ at $\theta$ always passes through the fixed point

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

If the curve $y = ax^{2} + bx + c, x \in R,$ passes through the point $(1, 2)$ and the tangent line to this curve at the origin is $y = x$,then the possible values of $a, b, c$ are:

If the points of contact of the tangents drawn from $(0,0)$ to the curve $y=x^2+3x+4$ are $(\alpha, \beta)$ and $(\gamma, \delta)$,then $\beta+\delta=$

Let $S$ be the set of all natural numbers $n$ for which the line $\frac{x}{a} + \frac{y}{b} = 2$ is a tangent to the curve $\left(\frac{x}{a}\right)^n + \left(\frac{y}{b}\right)^n = 2$ at the point $(a, b)$,where $ab \neq 0$. Then: