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A chord PQ of the rectangular hyperbola xy = a² cuts the x-axis at A. C is the midpoint of PQ, and O is the origin. What type of triangle is triangle ACO?
- equilateral
- isosceles
- right angled
- right isosceles
Correct answer: isosceles
Solution
For the rectangular hyperbola, the midpoint C of a chord is equidistant from where the chord meets the x-axis (A) and from the origin O, so CA = CO and triangle ACO is isosceles.
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