If the distance between the foci of an ellipse is $6$ and the length of the minor axis is $8$,then the eccentricity is

Let $S = 0$ be an ellipse whose vertices are the extremities of the minor axis of the ellipse $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ where $a > b$. If $S = 0$ passes through the foci of $E$,then its eccentricity is (considering the eccentricity of $E$ as $e$).

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:

$A$ point $(4, -1)$ lies on an ellipse whose axes are parallel to the coordinate axes. If the line $x + 4y - 10 = 0$ is tangent to the ellipse at this point,find its equation $(a > b)$.

Given the base of a triangle and the sum of its other two sides,the locus of the center of its incircle is:

The equations of the tangents to the ellipse $9x^2 + 16y^2 = 144$ which pass through the point $(2, 3)$ are