If the equation ax^2 + 2hxy + by^2 = 0 repres | vedclass

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Question

(A) Given the homogeneous equation of the second degree: $ax^2 + 2hxy + by^2 = 0$. Dividing by $x^2$,we get $a + 2h(\frac{y}{x}) + b(\frac{y}{x})^2 =

Vedclass · Accepted Answer

$m_1 + m_2 = \frac{-2h}{b}$ and $m_1m_2 = \frac{a}{b}$

Vedclass · Answer

(A) Given the homogeneous equation of the second degree: $ax^2 + 2hxy + by^2 = 0$. Dividing by $x^2$,we get $a + 2h(\frac{y}{x}) + b(\frac{y}{x})^2 = 0$. Let $m = \frac{y}{x}$,then $bm^2 + 2hm + a = 0$. This is a quadratic equation in $m$ with roots $m_1$ and $m_2$. By the properties of roots of a quadratic equation,the sum of roots $m_1 + m_2 = \frac{-(	ext{coefficient of } m)}{	ext{coefficient of } m^2} = \frac{-2h}{b}$. The product of roots $m_1m_2 = \frac{	ext{constant term}}{	ext{coefficient of } m^2} = \frac{a}{b}$. Thus,the correct relation is $m_1 + m_2 = \frac{-2h}{b}$ and $m_1m_2 = \frac{a}{b}$.

If the equation $ax^2 + 2hxy + by^2 = 0$ represents two lines $y = m_1x$ and $y = m_2x$,then

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