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The slopes of the lines represented by x...

The slopes of the lines represented by `x^(2) + 2hxy + 2y^(2) = 0` are in the ratio 1 : 2, then find 'h'.

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To solve the problem, we need to find the value of \( h \) such that the slopes of the lines represented by the equation \( x^2 + 2hxy + 2y^2 = 0 \) are in the ratio \( 1:2 \). ### Step-by-Step Solution: 1. **Understand the Equation**: The given equation is \( x^2 + 2hxy + 2y^2 = 0 \). This represents two straight lines through the origin. 2. **Assume Slopes**: Let the slopes of the two lines be \( m_1 \) and \( m_2 \). We know that the slopes are in the ratio \( 1:2 \), which can be expressed as: \[ ...
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