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 of the pair of straight lines passing through the point $(1, 1)$ and perpendicular to the pair of lines $3x^2 + 11xy - 4y^2 = 0$ is $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ (where the constant term is $12$),then find the value of $2(a - h + b - g + f - 12)$.

If the sum of the slopes of the lines represented by the equation $x^2 - 2xy \tan A - y^2 = 0$ is $4$,then $\angle A = $

If the angles made by the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ with the $X$-axis are $\alpha$ and $\beta$, then $\tan(\alpha + \beta)$ is

The locus of a point which moves such that its distance from the $x$-axis is twice its distance from the line $x-y=0$ is

If two lines represented by the equation $x^2 - (1 + \sqrt{3})xy + \sqrt{3}y^2 = 0$ make angles $\alpha$ and $\beta$ with the $X$-axis, then find the value of $\tan(\alpha + \beta)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module