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

At which point on the curve $9y^2 = x^3$ does the normal to the curve make equal intercepts with the axes?

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:

The length of the subtangent to the curve $\sqrt{x} + \sqrt{y} = 3$ at the point $(4, 1)$ is

The equation of the normal to the curve $y = \sin \left( \frac{\pi x}{2} \right)$ at $(1, 1)$ is

$f(x)$ is a continuous function on $\mathbb{R}$ and $y=f(x)$ is a curve. If $(\alpha, \beta)$ is a point such that $\beta=f(\alpha)$ and $p\alpha+m\beta+n=0$ $(p \neq 0, m \neq 0)$,then which one of the following is true?