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Find the equation of the common tangent to the two ellipses x²/(a² + b²) + y²/b² = 1 and x²/a² + y²/(a² + b²) = 1.

1. by = ax + sqrt(a⁴ + a²*b² + b⁴)
2. by = ax - sqrt(a⁴ + a²*b² + b⁴)
3. ay = bx - sqrt(a⁴ + a²*b² + b⁴)
4. ay = bx + sqrt(a⁴ - a²*b² + b⁴)

Correct answer: by = ax + sqrt(a⁴ + a²*b² + b⁴)

Solution

Matching the tangency conditions of both ellipses gives m = a/b and c² = a⁴ + a²*b² + b⁴, so by = ax + sqrt(a⁴ + a²*b² + b⁴).

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