List of top Mathematics Questions on Ellipse asked in AP EAPCET

Area of the quadrilateral formed by joining the extremities of the major axis and minor axis of the ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] is \(8\sqrt3\). If the distance between its foci is \(4\sqrt2\), then the eccentricity of the ellipse is
If the distance between the foci of an ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] is \(6\) and the distance between its directrices is \(10\), then the equation of one of the tangents of the ellipse drawn parallel to the line \[ y=\sqrt2\,x+5 \] is
If the ends of the major axis \(A'\) and \(A\) of the ellipse \[ \frac{(x-2)^2}{a^2}+\frac{(y-3)^2}{b^2}=1 \] are respectively at distances \(9\) and \(3\) units from a directrix \(L\), then the foci of the ellipse are:
The equation of the tangent to the ellipse \[ \frac{x^2}{16}+\frac{y^2}{9}=1 \] which is parallel to the line \[ 3x+4y+5=0 \] is

The product of perpendiculars from the two foci of the ellipse $$ \frac{x^2}{9} + \frac{y^2}{25} = 1 $$ on the tangent at any point on the ellipse is: 

Tangents are drawn from point $ (1, 1) $ to the ellipse $ x^2 + y^2 + 10x + 8y - 23 = 0 $. If $ m_1, m_2 $ (with $ m_1>m_2 $) are the slopes of these tangents, then with respect to the given ellipse, the point $ P(m_1, m_2) $ lies:
If the latus rectum of an ellipse is equal to half of the minor axis, then its eccentricity is:
The distance between the directrices of the ellipse \[ \frac{x^2}{36}+\frac{y^2}{20}=1 \] is
If the angle between the straight lines joining the foci and the ends of the minor axis of the ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] is \(90^\circ\), then its eccentricity is
The focal distances of the point \(\left(\dfrac{4}{\sqrt{5}},\dfrac{3}{\sqrt{5}}\right)\) on the ellipse \(\dfrac{x^2}{4}+\dfrac{y^2}{9}=1\) are
Find the distance between the directrices of the ellipse: \[ \frac{x^2}{36} + \frac{y^2}{20} = 1 \]