If the coordinates of two points $A$ and $B$ are $(\sqrt{7}, 0)$ and $(-\sqrt{7}, 0)$ respectively and $P$ is any point on the conic $9x^{2} + 16y^{2} = 144$,then $PA + PB$ is equal to

Let a line $L$ pass through the point of intersection of the lines $bx + 10y - 8 = 0$ and $2x - 3y = 0$,where $b \in R - \{\frac{4}{3}\}$. If the line $L$ also passes through the point $(1, 1)$ and touches the circle $17(x^2 + y^2) = 16$,then the eccentricity of the ellipse $\frac{x^2}{5} + \frac{y^2}{b^2} = 1$ is:

The equation $\frac{x^2}{2 - r} + \frac{y^2}{r - 5} + 1 = 0$ represents an ellipse,if

The eccentricity of the conic $36x^2 + 144y^2 - 36x - 96y - 119 = 0$ is

Find the coordinates of the foci,the vertices,the length of the major axis,the minor axis,the eccentricity,and the length of the latus rectum of the ellipse $\frac{x^{2}}{100}+\frac{y^{2}}{400}=1$.

The position of the point $(1, 3)$ with respect to the ellipse $4x^2 + 9y^2 - 16x - 54y + 61 = 0$ is: