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Find the equation of the largest circle centred at (1, 0) that can be inscribed in the ellipse x² + 4y² = 16.

1. (x - 1)² + y² = 11/3
2. (x + 1)² + y² = 11/3
3. (x - 1)² + y² = 13/3
4. (x + 1)² + y² = 13/3

Correct answer: (x - 1)² + y² = 11/3

Solution

Minimising the distance from (1,0) to the ellipse gives a minimum squared distance of 11/3, so the largest inscribed circle has radius² = 11/3.

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