Area of the quadrilaterals formed by drawing tangents at the ends of latus recta of $\frac{{{x^2}}}{4} + \frac{{{y^2}}}{1} = 1$ is
$\frac{{16}}{{\sqrt 3 }}$
$\frac{{8}}{{\sqrt 3 }}$
$\frac{{4}}{{\sqrt 3 }}$
$4\sqrt 3 $
An ellipse is drawn by taking a diameter of the circle ${\left( {x - 1} \right)^2} + {y^2} = 1$ as its semi-minor axis and a diameter of the circle ${x^2} + {\left( {y - 2} \right)^2} = 4$ is semi-major axis. If the center of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is :
The equations of the common tangents to the ellipse, $ x^2 + 4y^2 = 8 $ $\&$ the parabola $y^2 = 4x$ can be
The equation of the ellipse whose one of the vertices is $(0,7)$ and the corresponding directrix is $y = 12$, is
The centre of the ellipse $4{x^2} + 9{y^2} - 16x - 54y + 61 = 0$ is
The equation $\frac{{{x^2}}}{{2 - r}} + \frac{{{y^2}}}{{r - 5}} + 1 = 0$ represents an ellipse, if