The length of the latus rectum of $16x^2 + 25y^2 = 400$ is

The equation of the ellipse whose one focus is at $(4, 0)$ and whose eccentricity is $4/5$,is

If $P$ is a point on $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ with foci $S$ and $S^{\prime}$,then the maximum area of $\triangle S P S^{\prime}$ is

The length of the latus rectum of the ellipse $16x^2 + 25y^2 = 400$ is

If $\tan \theta_1 \times \tan \theta_2 = -\frac{a^2}{b^2}$,then the chord joining $2$ points $\theta_1$ and $\theta_2$ on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ will subtend a right angle at

Find the number of real tangents that can be drawn from the point $(3, 5)$ to the ellipses $3x^2 + 5y^2 = 32$ and $25x^2 + 9y^2 = 450$.