An ellipse is drawn by taking a diameter of circle {left( {x - 1} right)^2} + {y^2} = 1 as its semi-

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10-2. Parabola, Ellipse, Hyperbola

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An ellipse is drawn by taking a diameter of the circle ${\left( {x - 1} \right)^2} + {y^2} = 1$ as its semi-minor axis and a diameter of the circle ${x^2} + {\left( {y - 2} \right)^2} = 4$ is semi-major axis. If the center of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is :

A

$4{x^2} + {y^2} = 4$

B

$\;{x^2} + 4{y^2} = 8$

C

$\;4{x^2} + {y^2} = 8$

D

$\;{x^2} + 4{y^2} = 16$

(AIEEE-2012)

Solution

Semi minor axis $b=2$

Semi major axis $a=4$

Equation of ellipse $=\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$

$\Rightarrow \frac{x^{2}}{16}+\frac{y^{2}}{4}=1$

$\Rightarrow \quad x^{2}+4 y^{2}=16.$

Standard 11

Mathematics

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