If a pair of lines x^{2}-2 p x y-y^{2}=0 and | vedclass

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

Question

(A) The equation of the pair of angle bisectors of the pair of lines $ax^{2}+2hxy+by^{2}=0$ is given by $\frac{x^{2}-y^{2}}{a-b} = \frac{xy}{h}$.For t

Vedclass · Accepted Answer

$p q=-1$

Vedclass · Answer

(A) The equation of the pair of angle bisectors of the pair of lines $ax^{2}+2hxy+by^{2}=0$ is given by $\frac{x^{2}-y^{2}}{a-b} = \frac{xy}{h}$.For the pair $x^{2}-2pxy-y^{2}=0$,we have $a=1, h=-p, b=-1$.The equation of the angle bisectors is $\frac{x^{2}-y^{2}}{1-(-1)} = \frac{xy}{-p}$,which simplifies to $\frac{x^{2}-y^{2}}{2} = \frac{xy}{-p}$.This gives $x^{2}-y^{2} = -\frac{2}{p}xy$,or $x^{2} + \frac{2}{p}xy - y^{2} = 0$.It is given that this pair is the same as $x^{2}-2qxy-y^{2}=0$.Comparing the coefficients of $xy$,we get $-2q = \frac{2}{p}$.Therefore,$pq = -1$.

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

Similar Questions

The equation of a pair of lines $y=px$ and $y=qx$ can be written as $(y-px)(y-qx)=0$. Then the equation of the pair of angle bisectors of the lines $x^2-4xy-5y^2=0$ is

If the pair of lines $ax^2-7xy-3y^2=0$ and $2x^2+xy-6y^2=0$ have exactly one line in common and $a$ is an integer,then the equation of the pair of bisectors of the angles between the lines $ax^2-7xy-3y^2=0$ is

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 pairs of straight 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:

If the equation $kx^2 - 5xy + 6y^2 + x - 3y = 0$ represents a pair of straight lines, then the coordinates of their point of intersection are

Vedclass Test Series

Exam Paper Generator

Online Exam Module