The eccentricity of the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$ is:

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

The point $(4, -3)$ with respect to the ellipse $4x^2 + 5y^2 = 1$ is:

The equation of the tangent of the ellipse $4x^2 + 9y^2 = 36$ at the end of the latus rectum lying in the second quadrant is:

The eccentric angle of the end point of the latus rectum of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is:

For which of the following curves is the line $x+\sqrt{3} y=2 \sqrt{3}$ a tangent at the point $\left(\frac{3 \sqrt{3}}{2}, \frac{1}{2}\right)$?