The combined equation of the lines passing through the origin and having slopes \(\frac{2}{3}\) and…
The combined equation of the lines passing through the origin and having slopes \(\frac{2}{3}\) and \(\frac{-2}{3}\) is
\(2 x^2-9 y^2=0\)
\(4 x^2-x y-9 y^2=0\)
\(4 x^2-9 y^2=0\)
\(4 x^2+x y-9 y^2=0\)
Solution
The equation of lines passes through origin having slopes \(\frac{2}{3}\) and \(-\frac{2}{3}\) are respectively \(2 x+3 y=0\) and \(2 x-3 y=0\), so combined equation is
\(\begin{array}{rlrl}
& & (2 x-3 y)(2 x+3 y) & =0 \\
\Rightarrow & 4 x^2-9 y^2 & =0.
\end{array}\)