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
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
- A
$\frac{{16}}{{\sqrt 3 }}$
- B
$\frac{{8}}{{\sqrt 3 }}$
- C
$\frac{{4}}{{\sqrt 3 }}$
- D
$4\sqrt 3 $
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Let $E_{1}: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, \mathrm{a}\,>\,\mathrm{b} .$ Let $\mathrm{E}_{2}$ be another ellipse such that it touches the end points of major axis of $E_{1}$ and the foci $E_{2}$ are the end points of minor axis of $E_{1}$. If $E_{1}$ and $E_{2}$ have same eccentricities, then its value is :
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- [JEE MAIN 2021]
An ellipse having foci at $(3, 3) $ and $(- 4, 4)$ and passing through the origin has eccentricity equal to
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Statement $-1$ : If two tangents are drawn to an ellipse from a single point and if they are perpendicular to each other, then locus of that point is always a circle
Statement $-2$ : For an ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ , locus of that point from which two perpendicular tangents are drawn, is $x^2 + y^2 = (a + b)^2$ .
Statement $-1$ : If two tangents are drawn to an ellipse from a single point and if they are perpendicular to each other, then locus of that point is always a circle
Statement $-2$ : For an ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ , locus of that point from which two perpendicular tangents are drawn, is $x^2 + y^2 = (a + b)^2$ .