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How many tangents to the curve 4x² - 9y² = 36 can be drawn that are perpendicular to the line 5x + 2y - 10 = 0?
- zero
- 1
- 2
- 4
Correct answer: zero
Solution
For x²/9 - y²/4 = 1, a tangent of slope m needs a² m² - b² > 0; with m = 2/5, a² m² = 9*(4/25) = 1.44 < b² = 4, so no such tangent exists.
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