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 :

Engineering

Mathematics

Standard Ellipse

Question

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 :

x² + y² – 6y + 5 = 0

x² + y² – 6y + 7 = 0

x² + y² – 6y – 7 = 0

x² + y² – 6y – 5 = 0

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r² = 7 + 9

r² = 16

r = 4

$\Rightarrow$ (x – 0)² + (y – 3)² = 16

$\Rightarrow$ x² + y² – 6y – 7 = 0.