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For the one-parameter family of lines a(2x + y + 4) + b(x - 2y - 3) = 0, how many lines in the family are at a distance √10 from the point P(2, -3)?

1. 0
2. 1
3. 2
4. 4

Correct answer: 1

Solution

The equation represents a family of lines parameterized by a and b. To find the number of lines at a specific distance from point P(2, -3), we can derive the distance formula from the line equation and set it equal to the given distance, resulting in a quadratic equation that has one solution, indicating that there is exactly one line at the specified distance.

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