The length of $x$-intercept made by pair of lines $2 x^2+x y-6 y^2-2 x+17 y-12=0$ is

Question

Aicharya · Accepted Answer

$2 x^2+x y-6 y^2-2 x+17 y-12=0$
Comparing with $\begin{aligned} & a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 \\ & \Rightarrow a=2, g=-1, c=-12 \end{aligned}$
Length of $x$-intercept $=\frac{2 \sqrt{g^2-a c}}{a}=\frac{2 \sqrt{1-2(-12)}}{2}=5 .$

The length of $x$-intercept made by pair of lines $2 x^2+x y-6 y^2-2 x+17 y-12=0$ is

Solution