Which of the following pair of straight lines intersect at right angles?
Which of the following pair of straight lines intersect at right angles?
\(2 x^2=y(x+2 y)\)
\((x+y)^2=x(y+3 x)\)
\(2 y(x+y)=x y\)
\(y= \pm 2 x\)
Solution
For perpendicular pairs, \(a+b=0\)
Now for pairs,
\(\begin{aligned}
& 2 x^2=y(x+2 y) \\
\Rightarrow \quad & 2 x^2-2 y^2-x y=0
\end{aligned}\)
Coefficient of \(x^2+\) coefficient of \(y^2\)
\(=2+-2=0\)
So, there are perpendicular lines.