The least intercept made by a tangent to the ellipse $\frac{x^2}{64}+\frac{y^2}{49}=1$ with the coordinate axes is

If $P$ is any point on the ellipse $\frac{x^2}{25} + \frac{y^2}{9} = 1$ and $S, S^{\prime}$ are its foci,then the maximum area (in sq. units) of $\Delta SPS^{\prime} =$

The coordinates of the foci of the ellipse $16x^{2} + 9y^{2} = 144$ are

The parametric representation of a point on the ellipse whose foci are $(-1,0)$ and $(7,0)$ and eccentricity $1/2$ is

Let $(x, y)$ be a variable point on the curve $4x^2 + 9y^2 - 8x - 36y + 15 = 0$. Then,$\min (x^2 - 2x + y^2 - 4y + 5) + \max (x^2 - 2x + y^2 - 4y + 5)$ is

Consider the parabola $P : y^2 = 4x$ and the ellipse $E : \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Let the line segment joining the points of intersection of $P$ and $E$ be their common latus rectum. If the eccentricity of $E$ is $e$, then $e^2 + 2\sqrt{2}$ is equal to . . . . . .