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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?

1. Its centre lies on the line y = x.
2. The given hyperbola is a rectangular hyperbola.
3. The distance between its two directrices is sqrt(2).
4. 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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