The acute angle between the pair of tangents drawn to the ellipse $2 x^{2}+3 y^{2}=5$ from the point $(1,3)$ is.
$\tan ^{-1}\left(\frac{16}{7 \sqrt{5}}\right)$
$\tan ^{-1}\left(\frac{24}{7 \sqrt{5}}\right)$
$\tan ^{-1}\left(\frac{32}{7 \sqrt{5}}\right)$
$\tan ^{-1}\left(\frac{3+8 \sqrt{5}}{35}\right)$
If tangents are drawn from the point ($2 + 13cos\theta , 3 + 13sin\theta $) to the ellipse $\frac{(x-2)^2}{25} + \frac{(y-3)^2}{144} = 1,$ then angle between them, is
The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{5} = 1$, is .............. $\mathrm{sq. \,units}$
The equation of the ellipse whose vertices are $( \pm 5,\;0)$ and foci are $( \pm 4,\;0)$ is
If $P_1$ and $P_2$ are two points on the ellipse $\frac{{{x^2}}}{4} + {y^2} = 1$ at which the tangents are parallel to the chord joining the points $(0, 1)$ and $(2, 0)$, then the distance between $P_1$ and $P_2$ is
Let $A = \left\{ {\left( {x,y} \right):\,y = mx + 1} \right\}$
$B = \left\{ {\left( {x,y} \right):\,\,{x^2} + 4{y^2} = 1} \right\}$
$C = \left\{ {\left( {\alpha ,\beta } \right):\,\left( {\alpha ,\beta } \right) \in A\,\,and\,\,\left( {\alpha ,\beta } \right) \in B\,\,and\,\alpha \, > 0} \right\}$ .
If set $C$ is singleton set then sum of all possible values of $m$ is