The position of the point $(4, -3)$ with respect to the ellipse $2x^2 + 5y^2 = 20$ is

The longest distance of the point $(a, 0)$ from the curve $2x^2+y^2=2x$ is

If tangents are drawn from point $P(3 \sin \theta + 4 \cos \theta, 3 \cos \theta - 4 \sin \theta)$ where $\theta = \frac{\pi}{8}$ to the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$,then the angle between the tangents is:

Find the equation of the ellipse whose vertices are $(\pm 13, 0)$ and foci are $(\pm 5, 0)$.

On the ellipse $\frac{x^{2}}{8}+\frac{y^{2}}{4}=1$,let $P$ be a point in the second quadrant such that the tangent at $P$ to the ellipse is perpendicular to the line $x+2y=0$. Let $S$ and $S'$ be the foci of the ellipse and $e$ be its eccentricity. If $A$ is the area of the triangle $SPS'$,then the value of $(5-e^{2}) \cdot A$ is:

The equation of the normal at the point $(0, 3)$ of the ellipse $9x^2 + 5y^2 = 45$ is