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If the slope of one of the pairs of line...

If the slope of one of the pairs of lines represented by equation `a^(3) x^(2) + 2hxy + b^(3) y^(2) = 0` is square of the other, then prove that
`ab(a+ b) = - 2h. `

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To prove that \( ab(a + b) = -2h \) given that the slope of one of the pairs of lines represented by the equation \( a^3 x^2 + 2hxy + b^3 y^2 = 0 \) is the square of the other, we will follow these steps: ### Step 1: Rewrite the Equation We start with the equation of the pair of lines: \[ a^3 x^2 + 2hxy + b^3 y^2 = 0 \] To analyze the slopes, we can divide the entire equation by \( x^2 \): ...
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