If the slope of one of the lines represented | vedclass

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

Question

(C) Let the slopes of the two lines be $m_1$ and $m_2$. Given $m_2 = \lambda m_1$.From the equation $ax^2 + 2hxy + by^2 = 0$,we have $m_1 + m_2 = -\fr

Vedclass · Accepted Answer

$4\lambda h^2 = ab(1 + \lambda)^2$

Vedclass · Answer

(C) Let the slopes of the two lines be $m_1$ and $m_2$. Given $m_2 = \lambda m_1$.From the equation $ax^2 + 2hxy + by^2 = 0$,we have $m_1 + m_2 = -\frac{2h}{b}$ and $m_1 m_2 = \frac{a}{b}$.Substituting $m_2 = \lambda m_1$ in the sum: $m_1(1 + \lambda) = -\frac{2h}{b} \Rightarrow m_1 = -\frac{2h}{b(1 + \lambda)}$.Substituting $m_2 = \lambda m_1$ in the product: $\lambda m_1^2 = \frac{a}{b} \Rightarrow m_1^2 = \frac{a}{b\lambda}$.Equating the squares: $\left(-\frac{2h}{b(1 + \lambda)}\right)^2 = \frac{a}{b\lambda}$.$\frac{4h^2}{b^2(1 + \lambda)^2} = \frac{a}{b\lambda}$.$4\lambda h^2 = ab(1 + \lambda)^2$.

If the slope of one of the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ is $\lambda$ times that of the other,then:

Similar Questions

If the equation $hxy + gx + fy + c = 0$ represents a pair of straight lines,then

The difference of the slopes of the lines represented by the equation ${x^2}(\sec^2 \theta - \sin^2 \theta) - 2xy \tan \theta + y^2 \sin^2 \theta = 0$ is:

If an equation $hxy + gx + fy + c = 0$ represents a pair of lines,then

The area of the triangle formed by the lines $3x^2 - 4xy + y^2 = 0$ and $2x - y = 6$ is:

The equations of the lines represented by the equation ${x^2} - 5xy + 6{y^2} = 0$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module