TS EAMCET 2020 (Online) 11th September Morning Shift | Ellipse Question 64 | Mathematics

If the sum of the distances from the foci to the centre $O(0,0)$ of an ellipse is $8 \sqrt{6}$ units and the area of the smallest rectangle in which that ellipse is inscribed is 80 sq. units, then the equation of such an ellipse is

$\frac{x^2}{100}+\frac{y^2}{64}=1$

$\frac{x^2}{100}+\frac{y^2}{16}=1$

$\frac{x^2}{10}+\frac{y^2}{4}=1$

$\frac{x^2}{100}+\frac{y^2}{4}=1$

TS EAMCET 2020 (Online) 11th September Morning Shift

MCQ (Single Correct Answer)

-0

The equation of the ellipse with directrix $3 x+4 y-5=0$, focus $(1,2)$ and eccentricity $1 / 2$, is

$x^2+84 y^2-24 x y-360 y+170 x+475=0$

$91 x^2+84 y^2-24 x y-170 x-360 y+475=0$

$91 x^2+84 y^2-24 x y-170 x+360 y+475=0$

$91 x^2+84 y^2-24 x y-170 x-360 y-475=0$

TS EAMCET 2020 (Online) 10th September Evening Shift

MCQ (Single Correct Answer)

-0

The ellipse having its foci $(0, \pm 1)$ and major axis of length $\sqrt{5}$ is

$20 x^2+4 y^2=5$

$36 x^2+20 y^2=45$

$4 x^2+20 y^2=5$

$20 x^2+36 y^2=45$

TS EAMCET 2020 (Online) 10th September Evening Shift

MCQ (Single Correct Answer)

-0

An ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with eccentricity $\frac{2 \sqrt{2}}{3}$ is inscribed in a circle $x^2+y^2=18$ such that the length of its major axis is equal to the diameter of this circle. The locus of the poles of all the tangents of the circle with respect to the ellipse is

$x^2+y^2=\frac{8}{9}$

$18 x+\frac{2 y}{9}=1$

$\frac{x^2}{18}+\frac{y^2}{9}=1$

$\frac{x^2}{18}+\frac{9 y^2}{2}=1$

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