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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

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x² + y² - 6y + 7 = 0

x² + y² - 6y - 5 = 0

x² + y² - 6y + 5 = 0

x² + y² - 6y - 7 = 0

answer is A.

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Detailed Solution

Foci $= (\pm ae, 0) = (\pm \sqrt{7}, 0)$ ; radius = 4
Equation of circle having centre (0,3) and radius 4 is x² + ( y - 3)² = 16

$∴ x^{2} + y^{2} - 6 y - 7 = 0$

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