Ellipse

The eccentricity of the ellipse whose major axis is three times the minor axis is:

The equation of the ellipse with focus at \((\pm 5,0)\) and $\(x=\frac{36}{5}\) as one directrix is

The line \(3 x+4 y-5=0\) cuts the curve \(2 x^2+3 y^2=5\) at \(A\) and \(B\). If ' \(O\) ' is the origin, then \(\angle A O B=\)

Let $P$ be any point on the ellipse $7x^{2}+16y^{2}=112,S$ be a focus, $L$ be the correspondingdirectrix and $PM$ be the perpendicular distance from $P$ to directrix $L$. Then $\frac{SP}{PM}=$

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 it eccentricity is

If tangents are drawn to the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{5}=1$ at the ends of latus recta, then the area ofthe quadrilateral thus formed is

If a focal chord of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ meets its minor axis at the point $(0,3)$, then the perpendicular distance from the centre of the ellipse to this focal chord is

The equation of an ellipse in its standard form, given the distance between its foci is 2 units and the length of its latusrectum is $\frac{15}{2}$ units, is

Let F and $\mathrm{F}^1$ be the foci of the ellipse $\frac{x^2}{4}+\frac{y^2}{b^2}=1(b \lt 2)$ and $B$ is one end of the minor axis. If the area of the triangle $\mathrm{FBF}^1$ is $\sqrt{3}$ sq. units, then the…

The major and minor axes of an ellipse are along the $X$-axis and $Y$-axis respectively. If its latusrectum is of length 4 and the distance between the foci is $4 \sqrt{2}$, then the equation of that ellipse is

Let $E_1=\frac{x^2}{9}+\frac{y^2}{4}=1$ and $E_2=\frac{x^2}{d^2}+\frac{y^2}{b^2}=1$ be two ellipses and $\mathrm{R}$ be a rectangle with sides parallel to the coordinate axes. Let $E_1$ be inscribed ellipse in…

$A B$ is a line segment moving between the axes such that ' $A$ ' lies on $X$-axis and ' $B$ ' lies on $Y$-axis. If $P$ is a point on $A B$ such that $P A=b$ and $P B=a$, then the equation of locus of $P$ is