(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 $m = \frac{y}{x}$,then $bm^2+2hm+a=

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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 $m = \frac{y}{x}$,then $bm^2+2hm+a=0$. The roots of this quadratic equation are the slopes $m_1$ and $m_2$ of the lines. Given $h^2=ab$,the discriminant $D = (2h)^2 - 4ab = 4h^2 - 4ab = 4(h^2-ab) = 0$. Since the discriminant is zero,the roots are equal,i.e.,$m_1 = m_2$. Therefore,the ratio of the slopes is $m_1:m_2 = 1:1$.

Class 11 Mathematics Pair of straight lines Angle between the pair of straight lines, Condition for parallel and perpendicular lines

Easy

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

AP EAMCET 2021 All AP EAMCET

A
$1:2$
B
$2:1$
C
$2:3$
D
$1:1$

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Pair of straight lines

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Angle between the pair of straight lines, Condition for parallel and perpendicular lines

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

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