If h^2=ab,then the slopes of lines represente | vedclass

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(D) The given equation is $ax^2+2hxy+by^2=0$. Dividing by $x^2$,we get $b(\frac{y}{x})^2+2h(\frac{y}{x})+a=0$. Let $m = \frac{y}{x}$,so $bm^2+2hm+a=0$

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$1:1$

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(D) The given equation is $ax^2+2hxy+by^2=0$. Dividing by $x^2$,we get $b(\frac{y}{x})^2+2h(\frac{y}{x})+a=0$. Let $m = \frac{y}{x}$,so $bm^2+2hm+a=0$. The roots $m_1$ and $m_2$ represent the slopes of the lines. The quadratic formula gives $m = \frac{-2h \pm \sqrt{4h^2-4ab}}{2b}$. Since $h^2=ab$,the discriminant $4h^2-4ab = 0$. Thus,$m_1 = m_2 = -\frac{2h}{2b} = -\frac{h}{b}$. The ratio of the slopes is $m_1:m_2 = 1:1$.

If $h^2=ab$,then the slopes of lines represented by $ax^2+2hxy+by^2=0$ are in the ratio

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