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

The area (in sq. units) of the triangle formed by the tangent and normal drawn to the curve $(\frac{x}{3})^n+(\frac{y}{4})^n=2$ at $(3,4)$ and the $X$-axis is

If the lengths of the tangent,subtangent,normal and subnormal for the curve $y=x^2+x-1$ at the point $(1,1)$ are $a, b, c$ and $d$ respectively,then their increasing order is

The slope of the normal drawn at a point $P$ to the curve $y = x^3 - 10x^2 + 31x - 30$ is $-\frac{1}{14}$. Find the $x$-intercept of the tangent at point $P$, given that the $x$-coordinate of $P$ is an integer.

The point on the curve $y=x^2+4x+3$ which is closest to the line $y=3x+2$ is

$A$ straight line $L$ passing through the point $(2,3)$ bounds the minimum area with the curve $f(x) = x^2 - 4x + 6$. Find the equation of the tangent to the curve parallel to $L$.