Ellipse
Foci and Circle
Grade 11
Question:
<p>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:</p>
<p>(a) \(x^2 + y^2 - 6y + 5 = 0\)</p>
<p>(b) \(x^2 + y^2 - 6y - 7 = 0\)</p>
<p>(c) \(x^2 + y^2 - 6y + 7 = 0\)</p>
<p>(d) \(x^2 + y^2 - 6y - 5 = 0\)</p>
Step-by-Step Solution
Key Concept: Find the foci of the ellipse using \(c^2 = a^2 - b^2\), then use the distance from centre (0,3) to a focus as the radius.
<p>Answer: (b)</p>
Correct Answer: B