The eccentricity of the ellipse $4x^2 + 9y^2 + 8x + 36y + 4 = 0$ is

If the coordinates of two points $A$ and $B$ are $(\sqrt{7}, 0)$ and $(-\sqrt{7}, 0)$ respectively and $P$ is any point on the conic $9x^{2} + 16y^{2} = 144$,then $PA + PB$ is equal to

If the distance between the directrices is thrice the distance between the foci,then the eccentricity of the ellipse is

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

If $\alpha, \beta$ are the two real roots of the $4^{th}$ roots of unity and $\gamma, \delta$ are the other two roots,then the sum of the eccentricities of the conics $|z-\alpha|+|z-\beta|=4$ and $|z-\gamma|+|z-\delta|=6$ is

The area (in sq. units) of the triangle formed by the tangent and normal at a point $\left(\frac{a}{\sqrt{2}}, \frac{b}{\sqrt{2}}\right)$ to the curve $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and the $X$-axis is