An ellipse has $OB$ as semi-minor axis,$F$ and $F'$ as its foci,and the angle $\angle FBF'$ is a right angle. Then the eccentricity of the ellipse is

The tangents drawn from the point $P(3, 4)$ to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ touch the ellipse at points $A$ and $B$. The equation of the locus of a point which is equidistant from point $P$ and the line $AB$ is:

Find the area of the quadrilateral formed by the tangents at the endpoints of the latus rectum of the ellipse $x^2 + 2y^2 = 2$.

For what value of $c$ does the line $y = 4x + c$ touch the curve $\frac{x^2}{4} + y^2 = 1$? Find the number of possible values of $c$.

Consider the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$. Let $S(p, q)$ be a point in the first quadrant such that $\frac{p^2}{9}+\frac{q^2}{4}>1$. Two tangents are drawn from $S$ to the ellipse,of which one meets the ellipse at one end point of the minor axis and the other meets the ellipse at a point $T$ in the fourth quadrant. Let $R$ be the vertex of the ellipse with positive $x$-coordinate and $O$ be the center of the ellipse. If the area of the triangle $\triangle ORT$ is $\frac{3}{2}$,then which of the following options is correct?

Find the length of the latus rectum of the ellipse $\frac{x^2}{36} + \frac{y^2}{49} = 1$.