The equation of the line common to the pair o | vedclass

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

Question

(B) The given equations are:$(p^2-q^2) x^2+(q^2-r^2) xy+(r^2-p^2) y^2=0$  ...$(i)$$(l-m) x^2+(m-n) xy+(n-l) y^2=0$  ...(ii)For any equation of the for

Vedclass · Accepted Answer

$x-y=0$

Vedclass · Answer

(B) The given equations are:$(p^2-q^2) x^2+(q^2-r^2) xy+(r^2-p^2) y^2=0$  ...$(i)$$(l-m) x^2+(m-n) xy+(n-l) y^2=0$  ...(ii)For any equation of the form $Ax^2+Bxy+Cy^2=0$,if $A+B+C=0$,then $(x-y)$ is a factor of the equation.For equation $(i)$: $(p^2-q^2) + (q^2-r^2) + (r^2-p^2) = 0$. Thus,$(x-y)$ is a factor.For equation (ii): $(l-m) + (m-n) + (n-l) = 0$. Thus,$(x-y)$ is a factor.Since both equations represent a pair of lines passing through the origin and share the factor $(x-y)$,the common line is $x-y=0$.

The equation of the line common to the pair of lines $(p^2-q^2) x^2+(q^2-r^2) xy+(r^2-p^2) y^2=0$ and $(l-m) x^2+(m-n) xy+(n-l) y^2=0$ is

Similar Questions

If $ad \neq 0$ and two of the lines represented by $ax^3+3bx^2y+3cxy^2+dy^3=0$ are perpendicular,then

If an angular bisector of the coordinate axes is one of the lines of $x^2+2ax y+3y^2=0$,then the sum of all possible values of $a$ is

If the angles made by the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ with the $X$-axis are $\alpha$ and $\beta$, then $\tan(\alpha + \beta)$ is

For $\ell \in R$,the equation $(2 \ell-3) x^2+2 \ell xy-y^2=0$ represents a pair of distinct lines

If two lines represented by $ax^2+2hxy+by^2=0$ make angles $\alpha$ and $\beta$ with the positive direction of the $X$-axis,then $\tan(\alpha+\beta)=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module