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How many distinct straight lines can be drawn through the point (2, 3) such that, together with the coordinate axes, they enclose a triangle of area 12 square units?

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

Correct answer: 3

Solution

For line x/a + y/b = 1 through (2,3) with area (1/2)|ab| = 12, so |ab| = 24 and 2b+3a = ab. With ab = 24: (a-4)^2 = 0 gives one line (a=4). With ab = -24: a^2+8a-16 = 0 gives two real solutions. Total 3 lines.

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