If the lines represented by x^2-2hxy-y^2=0 ar | vedclass

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

Question

(C) The angle bisectors of two lines remain invariant under rotation of the lines by the same angle in opposite directions.Therefore,the bisectors of

Vedclass · Accepted Answer

$hx^2-hy^2+2xy=0$

Vedclass · Answer

(C) The angle bisectors of two lines remain invariant under rotation of the lines by the same angle in opposite directions.Therefore,the bisectors of the new lines are the same as the bisectors of the original lines $x^2-2hxy-y^2=0$.The equation of the angle bisectors for a pair of lines $ax^2+2hxy+by^2=0$ is given by $\frac{x^2-y^2}{a-b} = \frac{xy}{h}$.Here,$a=1$,$b=-1$,and the coefficient of $xy$ is $-2h$,so the coefficient of $xy$ in the formula is $2h' = -2h$,which means $h' = -h$.Substituting these values into the formula:$\frac{x^2-y^2}{1-(-1)} = \frac{xy}{-h}$$\frac{x^2-y^2}{2} = \frac{xy}{-h}$$-h(x^2-y^2) = 2xy$$-hx^2+hy^2 = 2xy$$hx^2-hy^2+2xy = 0$

If the lines represented by $x^2-2hxy-y^2=0$ are rotated about $(0,0)$ through an angle $\alpha$,one in the clockwise direction and the other in the counter-clockwise direction,then the combined equation of the bisectors of the angle between the lines thus obtained is

Similar Questions

The straight line passing through $(-1, 1)$ and parallel to the common line of the pairs of lines given by $6x^2 - xy - 12y^2 = 0$ and $15x^2 + 14xy - 8y^2 = 0$ is:

If the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+\lambda y-8=0$ are concurrent,then the value of $\lambda$ is

Find the equation of the bisectors of the angles between the lines represented by the equation $2x^{2} - 7xy + 3y^{2} = 0$.

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:

The ratio in which the line $x+y-1=0$ divides the line segment joining the origin $(0,0)$ and the point of intersection of the lines represented by $2x^2-13xy-7y^2+x+23y-6=0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module