The equations of the latus rectum of the ellipse $9x^2 + 25y^2 - 36x + 50y - 164 = 0$ are

If the distance between the two foci of an ellipse is equal to its minor axis,then the eccentricity of the ellipse is:

If any tangent to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ makes intercepts of length $h$ and $k$ on the axes,then:

If $\tan \theta_1 \cdot \tan \theta_2 = -\frac{a^2}{b^2}$,then the chord joining two 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:

$A$ tangent having slope $m = -1/2$ to the ellipse $3x^2 + 4y^2 = 12$ intersects the $X$-axis and $Y$-axis at the points $A$ and $B$ respectively. If $O$ is the origin, then the area of $\Delta AOB$ is ...

$P$ is a variable point on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with $AA'$ as the major axis. Then the maximum value of the area of $\Delta APA'$ is