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The line y = mx + c touches the hyperbola x²/a² − y²/b² = 1 only if
Ac² = b²m² − a²
Bc² = a²m² + b²
Cc² = a²m² − b²
Dc² = a² + b²m²
Answer & Solution
Correct answer: C. c² = a²m² − b²
Substituting the line gives a quadratic in x whose discriminant vanishes when c² = a²m² − b².
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