If one of the lines in the pair of straight l | vedclass

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

Question

(C) The general equation of a pair of straight lines passing through the origin is $ax^2+2hxy+by^2=0$.If one of these lines bisects the angle between

Vedclass · Accepted Answer

$\{-10,2\}$

Vedclass · Answer

(C) The general equation of a pair of straight lines passing through the origin is $ax^2+2hxy+by^2=0$.If one of these lines bisects the angle between the coordinate axes,its equation is $y=x$ or $y=-x$.Substituting $y=x$ into the equation $ax^2+2hxy+by^2=0$,we get $ax^2+2hx^2+bx^2=0$,which implies $a+2h+b=0$,or $a+b=-2h$. Squaring both sides gives $(a+b)^2=4h^2$.Similarly,if $y=-x$,we get $ax^2-2hx^2+bx^2=0$,which implies $a-2h+b=0$,or $a+b=2h$. Squaring both sides gives $(a+b)^2=4h^2$.Thus,the condition for one of the lines to bisect the angle between the axes is $(a+b)^2=4h^2$.For the given equation $4x^2+6xy+ky^2=0$,we have $a=4$,$2h=6$ (so $h=3$),and $b=k$.Substituting these values into the condition $(a+b)^2=4h^2$:$(4+k)^2=4(3)^2$$(4+k)^2=36$$4+k = \pm 6$If $4+k=6$,then $k=2$.If $4+k=-6$,then $k=-10$.Therefore,$k \in \{-10, 2\}$.

If one of the lines in the pair of straight lines given by $4x^2+6xy+ky^2=0$ bisects the angle between the coordinate axes,then $k \in$

Similar Questions

$\left\{x \in R: \frac{2x-1}{x^3+4x^2+3x} \in R\right\}$ equals

The solution of the differential equation $\frac{dy}{dx} = \sin(x+y) \tan(x+y) - 1$ is

What is a soredium?

$\lim _{x \rightarrow 0} \frac{\tan ^3 x-\sin ^3 x}{x^5}$ is equal to

$A$ tension of $22 ~N$ is applied to a copper wire of cross-sectional area $0.02 ~cm^2$. The Young's modulus of copper is $1.1 \times 10^{11} ~N/m^2$ and the Poisson's ratio is $0.32$. The decrease in cross-sectional area will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module