The equations of the tangents of the ellipse $9{x^2} + 16{y^2} = 144$ which passes through the point $(2, 3)$ is
$y = 3,\;x + y = 5$
$y = - 3,\;x - y = 5$
$y = 4,\;x + y = 3$
$y = - 4,\;x - y = 3$
The ellipse $ 4x^2 + 9y^2 = 36$ and the hyperbola $ 4x^2 -y^2 = 4$ have the same foci and they intersect at right angles then the equation of the circle through the points of intersection of two conics is
The value of $\lambda $, for which the line $2x - \frac{8}{3}\lambda y = - 3$ is a normal to the conic ${x^2} + \frac{{{y^2}}}{4} = 1$ is
The normal at a point $P$ on the ellipse $x^2+4 y^2=16$ meets the $x$-axis at $Q$. If $M$ is the mid point of the line segment $P Q$, then the locus of $M$ intersects the latus rectums of the given ellipse at the points
If end points of latus rectum of an ellipse are vertices of a square, then eccentricity of ellipse will be -
If $\alpha $ and $\beta $ are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is