COMEDK · Maths · 14. Ellipse
The radius of the circle passes through the foci of a conic \(\dfrac{x^2}{16}+\dfrac{y^2}{9}=1\) and has its centre at \((0,3)\), then the diameter of the circle is ---
- A 8 units
- B 4 units
- C 7 units
- D \(2 \sqrt{12}\) units
Answer & Solution
Correct Answer
(A) 8 units
Step-by-step Solution
Detailed explanation
The given equation of the ellipse is \(\dfrac{x^2}{16} + \dfrac{y^2}{9} = 1\). Here \(a^2 = 16\) and \(b^2 = 9\). The eccentricity \(e\) is given by \(e = \sqrt{1 - \dfrac{b^2}{a^2}} = \sqrt{1 - \dfrac{9}{16}} = \sqrt{\dfrac{7}{16}} = \dfrac{\sqrt{7}}{4}\). The foci of the…
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