If the distance between the foci of an ellipse is $6$ and the distance between its directrices is $12$,then the length of its latus rectum is

If the focal distance of an endpoint of the minor axis of an ellipse (taking its axes as the $x$ and $y$ axes respectively) is $k$ and the distance between its foci is $2h$,then its equation is:

The minimum area of the triangle formed by any tangent to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with the coordinate axes is

Let a line $L$ pass through the point of intersection of the lines $bx + 10y - 8 = 0$ and $2x - 3y = 0$,where $b \in R - \{\frac{4}{3}\}$. If the line $L$ also passes through the point $(1, 1)$ and touches the circle $17(x^2 + y^2) = 16$,then the eccentricity of the ellipse $\frac{x^2}{5} + \frac{y^2}{b^2} = 1$ is:

Find the coordinates of the foci,the vertices,the lengths of the major and minor axes,and the eccentricity of the ellipse $9x^{2} + 4y^{2} = 36$.

Let $S(1,0)$ and $S^{\prime}(0,1)$ be the foci of an ellipse such that $SP+S^{\prime} P=2$ for any point $P$ on the ellipse. If $A(x_1, y_1)$ and $A^{\prime}(x_2, y_2)$ are the end points of the major axis of this ellipse,then $x_1+x_2=$