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

The area (in sq units) of the triangle formed by the normal drawn at the point $(1,0)$ on the curve $x=e^{\sin y}$ with the coordinate axes is

The equation of the tangent to the curve $y = \sin x$ at the point $(\pi, 0)$ is $......$.

For $h, k \in N$, let $P(h, k)$ be the point of intersection of the curves $x^2 y - x^3 = 8$ and $y^3 - x y^2 = 32$. If $\theta$ is the acute angle between these two curves at $P$, then $\tan \theta =$

The sum of the intercepts on the axes of the tangent to the curve $\sqrt{x} + \sqrt{y} = \sqrt{a}$ is equal to:

If the tangent to the curve $y = \frac{x}{x^2-3}$,$x \in R, (x \neq \pm \sqrt{3})$ at a point $(\alpha, \beta) \neq (0,0)$ on it,is parallel to the line $2x + 6y - 11 = 0$,then