A line passing through (1, 0) intersects the curve $2x^2+5y^2-7x=0$ in A and B then the angle substended by the line AB at the origin is

Given curve  $2x^2+5y^2-7x=0$ --(1)

Equation of line passing through (1, 0) is

$\begin{array}{l}y-0=m\left(x-1\right)\\ \Rightarrow y=mx-m\Rightarrow mx-y=m\\ \Rightarrow \frac{mx-y}{m}=1--\left(2\right)\\ Homogenizing\left(1\right)with\left(2\right)\\ 2x^2+5y^2-7x\left(1\right)=0\\ \Rightarrow 2x^2+5y^2-7x\left(\frac{mx-y}{m}\right)=0\end{array}$

$\begin{array}{l}\Rightarrow 2m{x}^2+5m{y}^2-7m{x}^2+7xy=0\\ co.eff{x}^2+co.eff{y}^2=2m+5m-7m=0\\ Thelinesare\perp r\\ \therefore \mathrm{Re}qiuredangleis\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.\end{array}$