The eccentricity of the conic $\frac{5}{r}=2+3 \cos \theta+4 \sin \theta$ is

The foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}$ coincide. Then,the value of $b^2$ is

If two curves $x^2-4y^2=2$ and $8x^2=40-my^2$ are orthogonal to each other,then $m=$

Let $PQ$ be a focal chord of the parabola $y^{2}=4x$ such that it subtends an angle of $\frac{\pi}{2}$ at the point $(3, 0)$. Let the line segment $PQ$ be also a focal chord of the ellipse $E: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, a^{2}>b^{2}$. If $e$ is the eccentricity of the ellipse $E$,then the value of $\frac{1}{e^{2}}$ is equal to

$PQ$ is a normal chord of the parabola $y^2 = 4ax$ at $P$,$A$ being the vertex of the parabola. Through $P$,a line is drawn parallel to $AQ$ meeting the $x$-axis in $R$. Then the length of $AR$ is:

$TP$ and $TQ$ are tangents to the parabola $y^2 = 4ax$ at $P$ and $Q$. If the chord $PQ$ passes through the fixed point $(-a, b)$,then the locus of $T$ is: