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A hyperbola is defined by | sqrt((x-3)² + (y-3)²) - sqrt((x-1)² + (y-1)²) | = 2. Which of the following statements about it is correct?
- Its centre lies on the line y = x.
- The given hyperbola is a rectangular hyperbola.
- The distance between its two directrices is sqrt(2).
- Its asymptotes are inclined at 45 deg to each other.
Correct answer: Its centre lies on the line y = x.
Solution
The foci are (3,3) and (1,1), both on y = x, so the centre (their midpoint) is (2,2), which lies on y = x.
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