The equation of straight line passing through the point of intersection of the lines represented by $x^2+4 x…
The equation of straight line passing through the point of intersection of the lines represented by $x^2+4 x y+3 y^2-$ $4 x-10 y+3=0$ and the point $(2,2)$ is
$2 x+3 y-10=0$
$3 x+2 y-10=0$
$2 x+y-6=0$
$x+2 y-6=0$
Solution
$x^2+4 x y+3 y^2-4 x-10 y+3=0$
Comparing with $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$
$\begin{aligned}
& \text { Point of intersection }=\left(\frac{b g-f h}{h^2-a b}, \frac{a f-g h}{h^2-a b}\right) \\
& \Rightarrow\left(x_1, y_1\right)=\left(\frac{3(-2)-(-5) 2}{4-3}, \frac{-5-(-2) 2}{4-3}\right)=(4,-1)
\end{aligned}$ Equation of lines passing $(4,-1)$ and $(2,2)$ is
$y+1=\frac{2+1}{2-4}(x-4) \Rightarrow 3 x+2 y-10=0$