Let $\mathrm{PQR}$ be a right angled isosceles triangle, right angled at $Q(2,1)$. If the equation of the…
- $3 x^2+8 x y-3 y^2-20 x-10 y+25=0$
- $3 x^2-8 x y-3 y^2-20 x-10 y-25=0$
- $3 x^2+8 x y-3 y^2+20 x+10 y+25=0$
- $3 x^2-8 x y-3 y^2+20 x+10 y-25=0$
Solution
$\Rightarrow \mathrm{m}_1=-\frac{1}{3}$ or 3
$\therefore \quad$ 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 $\mathrm{QR}=\mathrm{m}_2=3 \quad \ldots[\because \mathrm{PQ} \perp \mathrm{QR}]$
$\therefore \quad$ Equation of $\mathrm{QR}$ is
$\begin{aligned} & y-1=3(x-2) \\ & \Rightarrow 3 x-y-5=0\end{aligned}$
$\therefore \quad$ The combined equation of the lines is
$\begin{aligned} & (x+3 y-5)(3 x-y-5)=0 \\ & \Rightarrow 3 x^2-3 y^2+8 x y-20 x-10 y+25=0\end{aligned}$Asked in: MHT CET 2023 (13 May Shift 2)