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For the pair of straight lines given by x² + 2hxy + 2y² = 0, if the ratio of their slopes is 1: 2, what is the value of h?

1. ±1/2
2. ±3/2
3. ±1
4. ±3

Correct answer: ±3/2

Solution

The slopes of the lines represented by the equation can be derived from the coefficients of the quadratic terms. Given the ratio of the slopes is 1:2, we can set up an equation involving h, leading to the conclusion that h must equal ±3/2 to satisfy this ratio.

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