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

The equation of the normal to the curve $2x^{2} + y^{2} = 12$ at the point $(2, 2)$ is

If the tangent to the curve $x^{2/3} + y^{2/3} = a^{2/3}$ meets the $X$-axis at $A$ and $Y$-axis at $B$,then $AB =$

If $\theta$ is the angle between the curves $xy=2$ and $x^2+4y=0$,then $\tan \theta$ is equal to:

If all the normals drawn to the curve $y=\frac{1+3x^2}{3+x^2}$ at the points of intersection of $y=\frac{1+3x^2}{3+x^2}$ and $y=1$ pass through the point $(\alpha, \beta)$,then $3\alpha+2\beta=$

If $\theta$ is the angle between the curves $x^2-y^2=4$ and $y^2=3x$,then $\tan \theta=$