Find the points on the curve $\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$ at which the tangents are parallel to the $x$-axis.

Let $m$ be the slope of the normal $L$ drawn at $(1, 2)$ to the curve $x = t^2 - 7t + 7, y = t^2 - 4t - 10$ and $ax + by + c = 0$ be the equation of the normal $L$. If the $G$.$C$.$D$. of $(a, b, c)$ is $1$, then $m(a + b + c) =$

Find the equation of the normal to the curve $y = \frac{x-7}{(x-2)(x-3)}$ at the point where it cuts the $X$-axis.

For what value of $a$ do the curves $y = 1 - ax^2$ and $y = x^2$ intersect orthogonally?

If two curves $x=y^2$ and $xy=a^3$ cut each other orthogonally at a point,then $a^2$ is equal to

If the normal to the curve $y=f(x)$ at the point $(3,4)$ makes an angle $\left(\frac{3 \pi}{4}\right)^{C}$ with the positive $X$-axis,then $f^{\prime}(3)$ is equal to