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Find the radius of a circle that passes through both foci of the ellipse 9x² + 16y² = 144 and has its centre at (0, 3).

1. 1
2. 2
3. 3
4. 4

Correct answer: 4

Solution

The ellipse 9x²+16y²=144 simplifies to x²/16+y²/9=1. Here a=4, b=3, so c=sqrt(a²-b²)=sqrt(7). Foci are at (+-sqrt(7), 0). Distance from centre (0,3) to focus (sqrt(7),0) = sqrt((sqrt(7))² + 3²) = sqrt(7+9) = sqrt(16) = 4. So radius = 4.

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