Ellipse · Mathematics · COMEDK

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MCQ (Single Correct Answer)

1
The area of the region bounded by the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is
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2
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 ---
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3
If the distance between the foci is equal to the length of the latus rectum, then the eccentricity of the ellipse is
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4

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

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5

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

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6

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

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7

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

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8

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

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9

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

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10

If p is any point on the ellipse $${{{x^2}} \over {36}} + {{{y^2}} \over {16}} = 1$$, and S and S' are the foci, then $$PS + PS' = $$

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