Ellipse

The tangent and normal to the ellipse 3x2
+ 5y2
= 32 at the point P(2, 2) meet the x-axis at Q and R,
respectively. Then the area (in sq. units) of the triangle PQR is :

If the length of the latus rectum of an ellipse is 4 units and the distance between a focus an its nearest vertex on the major axis is \({3 \over 2}\) units, then its eccentricity is :

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate
axes and passing through the points (4, −1) and (−2, 2) is :

Consider an ellipse, whose center is at the origin and its major axis is along the x-axis. If its eccentricity is \({3 \over 5}\) and the distance between its foci is 6, then the area (in sq. units) of the quadrilatateral inscribed in the e...

The eccentricity of an ellipse whose centre is at the origin is \({1 \over 2}\). If one of its directrices is x = – 4, then the
equation of the normal to it at \(\left( {1,{3 \over 2}} \right)\) is :

If the tangent at a point on the ellipse \({{{x^2}} \over {27}} + {{{y^2}} \over 3} = 1\) meets the coordinate axes at A and B, and O is the origin, then the
minimum area (in sq. units) of the triangle OAB is :

The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse \({{{x^2}} \over 9} + {{{y^2}} \over 5} = 1\), is :

The locus of the foot of perpendicular drawn from the centre of the ellipse \({x^2} + 3{y^2} = 6\) on any tangent to it is :

The equation of the circle passing through the foci of the ellipse \({{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1\), and having centre at \((0,3)\) is :

An ellipse is drawn by taking a diameter of thec 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 centre of the ellip...

STATEMENT-1 : An equation of a common tangent to the parabola \({y^2} = 16\sqrt 3 x\) and the ellipse \(2{x^2} + {y^2} = 4\) is \(y = 2x + 2\sqrt 3\)
STATEMENT-2 :If line \(y = mx + {{4\sqrt 3 } \over m},\left( {m \ne 0} \right)\) is a com...

Equation of the ellipse whose axes of coordinates and which passes through the point \((-3,1)\) and has eccentricity \(\sqrt {{2 \over 5}}\) is :

The ellipse \({x^2} + 4{y^2} = 4\) is inscribed in a rectangle aligned with the coordinate axex, which in turn is inscribed in another ellipse that passes through the point \((4,0)\). Then the equation of the ellipse is :

A focus of an ellipse is at the origin. The directrix is the line \(x=4\) and the eccentricity is \({{1 \over 2}}\). Then the length of the semi-major axis is :

In the ellipse, the distance between its foci is \(6\) and minor axis is \(8\). Then its eccentricity is :

An ellipse has \(OB\) as semi minor axis, \(F\) and \(F\)' its focii and theangle \(FBF\)' is a right angle. Then the eccentricity of the ellipse is :

The eccentricity of an ellipse, with its centre at the origin, is \({1 \over 2}\). If one of the directrices is \(x=4\), then the equation of the ellipse is :