COMEDK 2025 Afternoon Shift | Ellipse Question 2 | Mathematics

The radius of the circle passes through the foci of a conic $\frac{x^2}{16}+\frac{y^2}{9}=1$ and has its centre at $(0,3)$, then the diameter of the circle is ---

7 units

$2 \sqrt{12}$ units

8 units

4 units

COMEDK 2025 Morning Shift

MCQ (Single Correct Answer)

-0

If the distance between the foci is equal to the length of the latus rectum, then the eccentricity of the ellipse is

$\frac{\sqrt{5}+1}{2}$

$\frac{1-\sqrt{5}}{2}$

$\frac{\sqrt{5}-1}{2}$

$\frac{1 \pm \sqrt{5}}{2}$

COMEDK 2024 Evening Shift

MCQ (Single Correct Answer)

-0

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

$$ \frac{16 \pi}{3} \text { sq units } $$

$$9 \pi$$ sq units

$$10 \pi$$ sq units

$$ \frac{9 \pi}{5} \text { sq units } $$

COMEDK 2024 Afternoon Shift

MCQ (Single Correct Answer)

-0

The points on the ellipse $$16 x^2+9 y^2=400$$ at which the ordinate decreases at the same rate at which the abscissa increases are

$$ \left(3, \frac{16}{3}\right) \text { and }\left(-3,-\frac{16}{3}\right) $$

$$ \left(-3,-\frac{16}{3}\right) \text { and }\left(-3, \frac{16}{3}\right) $$

$$ \left(-3, \frac{16}{3}\right) \text { and }\left(3,-\frac{16}{3}\right) $$

$$ \left(3, \frac{16}{3}\right) \text { and }\left(-3, \frac{16}{3}\right) $$

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