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The ellipse x² + 2y² = 4 touches the rectangular hyperbola xy = c at points P and Q. Which statement is correct?
- O, P and Q are collinear points (where O is the origin)
- c is an irrational number
- length of PQ is 2sqrt(3)
- length of PQ is 2sqrt(2)
Correct answer: O, P and Q are collinear points (where O is the origin)
Solution
Both the ellipse and hyperbola are symmetric under (x,y) -> (-x,-y), so the two contact points are P and -P; hence O, P, Q are collinear.
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