Mathematics - Circle Question with Solution | TestHub

Point of intersection of lines

$x-y=1$ and $2x+y=3$

$O$ is  $\left(\frac{4}{3},\frac{1}{3}\right)$

Slope of $OP=\frac{\frac{1}{3}+1}{\frac{4}{3}-1}=\frac{\frac{4}{3}}{\frac{1}{3}}=4$

Slope of tangent $=-\frac{1}{4}$

$\Rightarrow$ Equation of tangent :$y+1= -\frac{1}{4}\left(x-1\right)$

$\Rightarrow 4y+4=-x+1$

$\Rightarrow x+4y+3=0$