The joint equation of the pair of lines passi | vedclass

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

Question

(B) Let the two lines passing through the origin be $L_1$ and $L_2$. Since they form an equilateral triangle with the line $y=3$,the angle made by the

Vedclass · Accepted Answer

$3x^2-y^2=0$

Vedclass · Answer

(B) Let the two lines passing through the origin be $L_1$ and $L_2$. Since they form an equilateral triangle with the line $y=3$,the angle made by these lines with the $x$-axis must be $60^{\circ}$ and $120^{\circ}$.The slopes of these lines are $m_1 = 	an(60^{\circ}) = \sqrt{3}$ and $m_2 = 	an(120^{\circ}) = -\sqrt{3}$.The equations of the lines are $y = \sqrt{3}x$ and $y = -\sqrt{3}x$.Rearranging these,we get $\sqrt{3}x - y = 0$ and $\sqrt{3}x + y = 0$.The joint equation is given by $(\sqrt{3}x - y)(\sqrt{3}x + y) = 0$.Expanding this,we get $(\sqrt{3}x)^2 - y^2 = 0$,which simplifies to $3x^2 - y^2 = 0$.

The joint equation of the pair of lines passing through the origin and forming an equilateral triangle with the line $y=3$ is

Similar Questions

If one of the lines given by $6x^2 - xy + 4cy^2 = 0$ is $3x + 4y = 0$,then $c$ equals

If the slopes of the lines given by the equation $ax^{2} + 2hxy + by^{2} = 0$ are in the ratio $5:3$,then the ratio $h^{2}:ab$ is:

If the lines represented by the equation $4xy + 6x - 8y + c = 0$ form a rectangle with the coordinate axes,then the area of the rectangle (in sq. units) is

If one of the lines $ax^2 + 2hxy + by^2 = 0$ bisects the angle between the positive coordinate axes,then

$A$ second degree homogeneous equation in $x$ and $y$ always represents:

Vedclass Test Series

Exam Paper Generator

Online Exam Module