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A straight line that makes equal intercepts on the coordinate axes is tangent to the ellipse x²/16 + y²/9 = 1. Writing this line in the form a x + b y + c = 0, find the value of (a² + b²)/c².

1. 1/25
2. 2/25
3. 1/5
4. 2/5

Correct answer: 2/25

Solution

For line y = -x + k tangent to the ellipse, k² = a² m² + b² = 16*1 + 9 = 25; with a=1, b=1, c=-k, (a²+b²)/c² = 2/25.

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