Let \(\mathrm{PQR}\) be a right angled isosceles triangle, right angled at \(Q(2,1)\). If the equation of the line PR is \(2 x+y=3\), then the combined equation representing the pair of lines PQ and QR is

\(\Rightarrow \mathrm{m}_1=-\frac{1}{3}\) or 3
\(\therefore \) Equation of \(\mathrm{PQ}\) passing through point \(\mathrm{Q}(2,1)\) and having slope \(m_1=-\frac{1}{3}\) is
\(\begin{aligned} & y-1=-\frac{1}{3}(x-2) \\ & \Rightarrow x+3 y-5=0\end{aligned}\)
Slope of \(\mathrm{QR}=\mathrm{m}_2=3 \quad \ldots[\because \mathrm{PQ} \perp \mathrm{QR}]\)
\(\therefore \) Equation of \(\mathrm{QR}\) is
\(\begin{aligned} & y-1=3(x-2) \\ & \Rightarrow 3 x-y-5=0\end{aligned}\)
\(\therefore \) The combined equation of the lines is
\(\begin{aligned} & (x+3 y-5)(3 x-y-5)=0 \\ & \Rightarrow 3 x^2-3 y^2+8 x y-20 x-10 y+25=0\end{aligned}\)