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From the centre C of the rectangular hyperbola x² - y² = 9, a perpendicular CM is dropped onto the tangent at an arbitrary point of the curve, meeting the tangent at M; the line CM produced meets the curve at N. Find the product (CM)(CN).
- 9
- 3
- 18
- 81
Correct answer: 9
Solution
For the rectangular hyperbola x² - y² = a², the perpendicular from the centre to a tangent times the distance from the centre to where that line meets the curve equals a². Here a² = 9.
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