In an ellipse $9{x^2} + 5{y^2} = 45$, the distance between the foci is

If $P \equiv (x,\;y)$, ${F_1} \equiv (3,\;0)$, ${F_2} \equiv ( - 3,\;0)$ and $16{x^2} + 25{y^2} = 400$, then $P{F_1} + P{F_2}$ equals

In an ellipse the distance between its foci is $6$ and its minor axis is $8$. Then its eccentricity is

If $x^{2}+9 y^{2}-4 x+3=0, x, y \in R$, then $x$ and $y$ respectively lie in the intervals:

A circle has the same centre as an ellipse and passes through the foci $F_1 \& F_2$  of the ellipse, such that the two curves intersect in $4$  points. Let $'P'$  be any one of their point of intersection. If the major axis of the ellipse is $17 $ and  the area of the triangle $PF_1F_2$ is $30$, then the distance between the foci is :

Let $L$ is distance between two parallel normals of  , $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1,\,\,\,a > b$ then maximum value of $L$ is