Let $S$ and $S'$ be the foci of the ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$ and $P$ be a variable point on the ellipse. The maximum area of the triangle $PSS'$ is ............. square units.

The length of the chord of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$,whose mid-point is $(1, \frac{2}{5})$,is equal to:

The eccentric angle of the end point of the latus rectum of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is:

Let $A = \{(x, y) : y = mx + 1\}$,$B = \{(x, y) : x^2 + 4y^2 = 1\}$,and $C = \{(\alpha, \beta) : (\alpha, \beta) \in A \text{ and } (\alpha, \beta) \in B \text{ and } \alpha > 0\}$. If set $C$ is a singleton set,then the sum of all possible values of $m$ is:

Find the equation for the ellipse that satisfies the given conditions: Length of major axis $= 26$,foci $= (\pm 5, 0)$.

If $S$ is the focus of the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ lying on the positive $X$-axis and $P(\theta)$ is a point on the ellipse such that $SP=1$,then $\cos \theta=$