If one of the lines my^2 + (1 - m^2)xy - mx^2 | vedclass

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

Question

(A) The given pair of lines is $my^2 + (1 - m^2)xy - mx^2 = 0$.This can be rewritten as $-mx^2 + (1 - m^2)xy + my^2 = 0$,or $mx^2 - (1 - m^2)xy - my^2

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) The given pair of lines is $my^2 + (1 - m^2)xy - mx^2 = 0$.This can be rewritten as $-mx^2 + (1 - m^2)xy + my^2 = 0$,or $mx^2 - (1 - m^2)xy - my^2 = 0$.The lines $xy = 0$ represent the coordinate axes,$x = 0$ and $y = 0$.The angle bisectors of the lines $x = 0$ and $y = 0$ are given by $x^2 - y^2 = 0$,which implies $x = y$ and $x = -y$.If one of the lines $my^2 + (1 - m^2)xy - mx^2 = 0$ is a bisector,it must be either $x - y = 0$ or $x + y = 0$.For $x - y = 0$,the equation is $x^2 - xy - xy + y^2 = 0$ (not matching) or by substituting $y = x$ into the original equation:$m(x^2) + (1 - m^2)x^2 - mx^2 = 0 \Rightarrow (1 - m^2)x^2 = 0$,which implies $m^2 = 1$,so $m = \pm 1$.However,if $m = 1$,the equation becomes $y^2 - x^2 = 0$,i.e.,$(y - x)(y + x) = 0$,which are the bisectors of $xy = 0$.If $m = -1$,the equation becomes $-y^2 + 2xy + x^2 = 0$,which are not the bisectors.Thus,$m = \pm 1$. Given the options,$m = 1$ is the correct choice.

If one of the lines $my^2 + (1 - m^2)xy - mx^2 = 0$ is a bisector of the angle between the lines $xy = 0$,then $m$ is

Similar Questions

Find the point of intersection of the lines represented by $2x^2 - 7xy - 4y^2 - x + 22y - 10 = 0$.

The combined equation of the two lines $ax+by+c=0$ and $a'x+b'y+c'=0$ can be written as $(ax+by+c)(a'x+b'y+c')=0$. The equation of the angle bisectors of the lines represented by the equation $2x^2+xy-3y^2=0$ is:

If a pair of lines $x^{2}-2 p x y-y^{2}=0$ and $x^{2}-2 q x y-y^{2}=0$ are such that each pair bisects the angle between the other pair,then

The area of the triangle formed by the line $x + y = 3$ and the angle bisectors of the pair of lines $x^2 - y^2 + 2y = 1$ is:

If the bisectors of the lines $x^2 - 2pxy - y^2 = 0$ are $x^2 - 2qxy - y^2 = 0$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module