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Let P be a point on the hyperbola x²/a² - y²/b² = 1, and let N be the foot of the perpendicular from P to the transverse (x) axis. The tangent at P meets the transverse axis at T, and O is the centre. Find the value of OT * ON.
- e²
- a²
- b²
- b²/a²
Correct answer: a²
Solution
With P parametrised, ON = a sec t and OT = a cos t, so OT*ON = a² (a standard hyperbola property).
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