Find the equation of the normal to the curve $2y = 3 - x^2$ at the point $(1, 1)$.

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

If the tangent drawn at a point $P$ on the curve $y=3x^2-5x+7$ is parallel to its chord joining the points $(1, y_1)$ and $(2, y_2)$ on it, then the $x$-coordinate of the point $P$ is

The sum of the intercepts made by a tangent drawn to the curve $\left(\frac{x}{a}\right)^n + \left(\frac{y}{b}\right)^n = 2$ at the point $(a, b)$ on the coordinate axes is:

The equation of the tangent to the curve $y = \cos(x + y)$ for $-2\pi \leq x \leq 2\pi$,which is parallel to the line $x + 2y = 0$,is:

The normal to the curve $xy = 4$ at the point $(2,2)$ will meet the curve again at which point?