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Two families of straight lines y - 1 = m1(x - 3) and y - 3 = m2(x - 1) are perpendicular to each other (m1 * m2 = -1). Find the locus of their point of intersection.

1. x² + y² - 2x - 6y + 10 = 0
2. x² + y² - 4x - 4y + 6 = 0
3. x² + y² - 2x - 6y + 6 = 0
4. x² + y² - 4x - 4y - 6 = 0

Correct answer: x² + y² - 4x - 4y + 6 = 0

Solution

Setting (k-1)(k-3) = -(h-3)(h-1) and expanding gives h²+k²-4h-4k+6=0, which is option B.

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