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

The foci of the ellipse $25(x + 1)^2 + 9(y + 2)^2 = 225$ are at

Let $S$ and $S^{\prime}$ be the foci of an ellipse $E$ and $B$ be one end of its minor axis. Let $\angle S^{\prime} SB = \frac{\pi}{6}$ and $(2 \sqrt{3}, 1)$ be a point on $E$. If $X$-axis is the major axis and $Y$-axis is the minor axis of the ellipse $E$,then the sum of the squares of the lengths of major axis and minor axis is

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(0, \pm \sqrt{5})$,ends of minor axis $(\pm 1, 0)$.

If the normal at one end of a latus rectum of the ellipse $\frac{x^2}{32}+\frac{y^2}{b^2}=1$ passes through one end of the minor axis,then $\frac{e^4}{1-e^2}=$ (Here $e$ is the eccentricity of the ellipse)

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 $\frac{x^{2}}{100}+\frac{y^{2}}{400}=1$.