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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

Similar Questions

The value of $k$ so that the equation $2x^2 + 5xy + 3y^2 + 6x + 7y + k = 0$ represents a pair of straight lines is:

If the sum of the slopes of the lines given by $4x^2 + 2\lambda xy - 7y^2 = 0$ is equal to the product of the slopes,then $\lambda$ is equal to

The area of the triangle formed by the lines represented by $4x^2 - 9xy - 9y^2 = 0$ and the line $x = 2$ is

If the slope of one of the lines represented by $ax^2 + 2hxy + by^2 = 0$ is the square of the other,then:

If $ax^2-xy-3y^2-5x+20y+c=0$ represents a pair of lines passing through the point $(2,3)$,then $a-c=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module