If an ellipse with its axes as coordinate axes, $2 a$ and $2 b$ as the lengths of its major and minor axes respectively passes through the points $(2,2)$ and $(3,1)$, then $3 a^2+5 b^2=$

The values of $c$ such that the line $y=4 x+c$ touches the ellipse $\frac{x^2}{4}+\frac{y^2}{1}=1$ is

If the line $x \cos \alpha+y \sin \alpha=2 \sqrt{3}$ is a tangent to the ellipse $\frac{x^2}{16}+\frac{y^2}{8}=1$ and $\alpha$ is an acute angle, then $\alpha=$

If $x+\sqrt{3} y=3$ is the tangent to the ellipse $2 x^2+3 y^2=k$ at a point $P$, then the equation of the normal to this ellipse at $P$ is