COMEDK 2024 Afternoon Shift | Ellipse Question 3 | Mathematics

If an ellipse has an equation in the standard form and it passes through the points $$\left(\frac{5}{2}, \frac{\sqrt{6}}{4}\right)$$ and $$\left(-2, \frac{\sqrt{15}}{5}\right)$$ then the length of its latus rectum is

$$\frac{1}{10}$$

$$\frac{1}{\sqrt{10}}$$

$$\sqrt{\frac{10}{5}}$$

$$\frac{\sqrt{10}}{5}$$

COMEDK 2024 Morning Shift

MCQ (Single Correct Answer)

-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

$$\frac{x^2}{4}+\frac{y^2}{3}=1$$

$$\frac{x^2}{3}+\frac{y^2}{4}=1$$

$$\frac{x^2}{2}+\frac{y^2}{3}=1$$

$$\frac{x^2}{3}+\frac{y^2}{8}=1$$

COMEDK 2023 Evening Shift

MCQ (Single Correct Answer)

-0

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

$$ \frac{1}{\sqrt{2}} $$

$$ \frac{2 \sqrt{2}}{3} $$

$$ \frac{2}{\sqrt{3}} $$

$$ \frac{1}{\sqrt{3}} $$

COMEDK 2020

MCQ (Single Correct Answer)

-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

$${{\sqrt 3 } \over 2}$$

$${1 \over {\sqrt 2 }}$$

$${1 \over 2}$$

$${1 \over {\sqrt 3 }}$$

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