1
COMEDK 2024 Evening Shift
+1
-0

$$\text { The area of the region enclosed by the curve }\left\{(x, y): 4 x^2+25 y^2=100\right\} \text { is }$$

A
$$\frac{16 \pi}{3} \text { sq units }$$
B
$$9 \pi$$ sq units
C
$$10 \pi$$ sq units
D
$$\frac{9 \pi}{5} \text { sq units }$$
2
COMEDK 2024 Morning Shift
+1
-0

The equation of an ellipse, whose focus is $$(1,0)$$, directrix is $$x=4$$ and whose eccentricity is a root of the quadratic equation $$2 x^2-3 x+1=0$$, is

A
$$\frac{x^2}{4}+\frac{y^2}{3}=1$$
B
$$\frac{x^2}{3}+\frac{y^2}{4}=1$$
C
$$\frac{x^2}{2}+\frac{y^2}{3}=1$$
D
$$\frac{x^2}{3}+\frac{y^2}{8}=1$$
3
COMEDK 2023 Evening Shift
+1
-0

If the length of the major axis of an ellipse is 3 times the length of the minor axis, then its eccentricity is

A
$$\frac{1}{\sqrt{2}}$$
B
$$\frac{2 \sqrt{2}}{3}$$
C
$$\frac{2}{\sqrt{3}}$$
D
$$\frac{1}{\sqrt{3}}$$
4
COMEDK 2020
+1
-0

If the area of the auxillary circle of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1(a > b)$$ is twice the area of the ellipse, then the eccentricity of the ellipse is

A
$${{\sqrt 3 } \over 2}$$
B
$${1 \over {\sqrt 2 }}$$
C
$${1 \over 2}$$
D
$${1 \over {\sqrt 3 }}$$
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