QJEEM13Mae6c6: JEE Main 2013 Mathematics - Class 11 JEEM13Mae6c6 Solution: The equation of the circle passing through the foci of the…

Question

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The equation of the circle passing through the foci of the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

, and having centre at

(0, 3)

is :

Accepted Answer

From the given equation of ellipse, we have

a = 4, b = 3, e = \sqrt{1 - \frac{9}{16}}

\Rightarrow e = \frac{\sqrt{7}}{4}

Now, radius of this circle

= a^{2} = 16

\Rightarrow F o c i i = (\pm \sqrt{7}, 0)

Now equation of circle is

{(x - 0)}^{2} + {(y - 3)}^{2} = 16

x^{2} + y^{2} - 6 y - 7 = 0

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