If one of the lines given by k x^2 + x y - y^ | vedclass

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

Question

(B) The equation of the pair of lines is $k x^2 + x y - y^2 = 0$. Since the lines bisect the angle between the coordinate axes,their slopes must be $m

Vedclass · Accepted Answer

$0$ and $2$

Vedclass · Answer

(B) The equation of the pair of lines is $k x^2 + x y - y^2 = 0$. Since the lines bisect the angle between the coordinate axes,their slopes must be $m = \pm 1$. Substituting $y = mx$ into the equation,we get $k x^2 + x(mx) - (mx)^2 = 0$. Dividing by $x^2$ (assuming $x 
eq 0$),we get $k + m - m^2 = 0$. For $m = 1$,$k + 1 - 1^2 = 0 \Rightarrow k = 0$. For $m = -1$,$k - 1 - (-1)^2 = 0$ $\Rightarrow k - 1 - 1 = 0$ $\Rightarrow k = 2$. Thus,the values of $k$ are $0$ and $2$.

If one of the lines given by $k x^2 + x y - y^2 = 0$ bisects the angle between the coordinate axes,then the values of $k$ are

Similar Questions

The joint equation of a pair of straight lines passing through the origin and having slopes $(1+\sqrt{2})$ and $\left(\frac{1}{1+\sqrt{2}}\right)$ is $......$

The auxiliary equation of the lines passing through the origin and having slopes $\sqrt{3}+1$ and $\sqrt{3}-1$ is

The combined equation of the lines passing through the point $(3,4)$ and each making an angle $45^{\circ}$ with the line $x+y+1=0$ is

If angles made by lines $x^2 - 4xy - y^2 = 0$ with the positive direction of the $x$-axis are $\theta_1$ and $\theta_2$,then the value of $\sec^2(\theta_1 + \theta_2) + |\frac{1}{\tan \theta_1} + \frac{1}{\tan \theta_2}|$ is

The slopes of the lines represented by $6x^2 + 2hxy + y^2 = 0$ are in the ratio $2:3$,then $h =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module