If the normal to the curve $y = f(x)$ at the point $(3, 4)$ makes a positive angle of $3\pi /4$ with the $x$-axis,then $f'(3) = .....$

Find the condition that the curves $2x = y^2$ and $2xy = k$ intersect orthogonally.

The line which is parallel to the $x$-axis and intersects the curve $y = \sqrt{x}$ at an angle of $45^\circ$ is given by:

The curve $y=ax^3+bx^2+cx+5$ touches the $X$-axis at $(-2,0)$ and cuts the $Y$-axis at a point $Q$ where its gradient is $3$. Then the values of $a, b, c$ respectively are:

If the normal drawn at a point $P$ on the curve $3y = 6x - 5x^3$ passes through $(0,0)$,then the positive integral value of the abscissa of the point $P$ is

If the line $y=4x-5$ touches the curve $y^{2}=ax^{3}+b$ at the point $(2,3)$,then