If the slope of one line of the pair of lines | vedclass

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

Question

(C) The equation of the pair of lines is $ax^2 + 4xy + y^2 = 0$.Comparing this with $Ax^2 + 2Hxy + By^2 = 0$,we have $A = a$,$2H = 4$ (so $H = 2$),and

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) The equation of the pair of lines is $ax^2 + 4xy + y^2 = 0$.Comparing this with $Ax^2 + 2Hxy + By^2 = 0$,we have $A = a$,$2H = 4$ (so $H = 2$),and $B = 1$.Let the slopes of the two lines be $m_1$ and $m_2$.Then $m_1 + m_2 = -\frac{2H}{B} = -\frac{4}{1} = -4$ $(i)$.And $m_1 m_2 = \frac{A}{B} = \frac{a}{1} = a$ $(ii)$.Given that $m_1 = 3m_2$.Substituting this into $(i)$,we get $3m_2 + m_2 = -4$,which implies $4m_2 = -4$,so $m_2 = -1$.Then $m_1 = 3(-1) = -3$.Substituting these values into $(ii)$,we get $a = m_1 m_2 = (-3)(-1) = 3$.

If the slope of one line of the pair of lines represented by $ax^2 + 4xy + y^2 = 0$ is $3$ times the slope of the other line,then $a$ is

Similar Questions

The joint equation of a pair of lines passing through the point $(1, 4)$, where one line is parallel to the $X$-axis and the other makes an angle of $45^\circ$ with the positive direction of the $X$-axis, is:

If one of the lines in the pair of straight lines given by $4x^2+6xy+ky^2=0$ bisects the angle between the coordinate axes,then $k \in$

If $3x^{2} + xy - y^{2} - 3x + 6y + k = 0$ represents a pair of lines,then $k$ is equal to

Which among the following represents the combined equation of a pair of lines passing through the point $(1, 0)$ and parallel to the lines represented by $2x^2 - xy - y^2 = 0$?

The perpendiculars are drawn to lines $L_1$ and $L_2$ from the origin making an angle $\frac{\pi}{4}$ and $\frac{3 \pi}{4}$ respectively with the positive direction of the $X$-axis. If both the lines are at a unit distance from the origin,then their joint equation is

Vedclass Test Series

Exam Paper Generator

Online Exam Module