Equation of the tangent to the circle, at the point (1, - 1) ,...

Point of intersection of lines

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

$O$ is \left(\dfrac{4}{3}, \dfrac{1}{3}\right)$</p><p>Slope of$OP = \dfrac{\dfrac{1}{3} + 1}{\dfrac{4}{3} - 1} = \dfrac{\dfrac{4}{3}}{\dfrac{1}{3}} = 4$</p><p>Slope of tangent$= - \dfrac{1}{4}$</p><p>$⇒$Equation of tangent :$y + 1 = - \dfrac{1}{4}\left(x - 1\right)

$⇒ 4y + 4 = - x + 1$

$⇒ x + 4y + 3 = 0$