Let $F_1$ & $F_2$ be the foci of an ellipse $\frac{{{x^2}}}{4} + \frac{{{y^2}}}{9} = 1$ such that a ray from $F_1$ strikes the elliptical mirror at the point $P$ and get reflected. Then equation of angle bisector of the angle between incident ray and reflected ray can be
$y = x + \frac{5}{{\sqrt {13} }}$
$y = 2x - \frac{5}{{\sqrt {13} }}$
$x + y -5 = 0$
$3x -4y -5 = 0$
A chord $PQ$ of the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ subtends right angle at its centre. The locus of the point of intersection of tangents drawn at $P$ and $Q$ is-
The equations of the tangents of the ellipse $9{x^2} + 16{y^2} = 144$ which passes through the point $(2, 3)$ is
If the line $y = 2x + c$ be a tangent to the ellipse $\frac{{{x^2}}}{8} + \frac{{{y^2}}}{4} = 1$, then $c = $
The number of values of $c$ such that the straight line $y = 4x + c$ touches the curve $\frac{{{x^2}}}{4} + {y^2} = 1$ is
The eccentricity of the ellipse $4{x^2} + 9{y^2} + 8x + 36y + 4 = 0$ is