Question

What is Length of tangent?

Answer

Length of tangent: * If the equation of the circle is$x^2+y^2=r^2,$ then the length of the tangent to the circle from point P(x₁, y₁) is given by$PT=\sqrt{x_1^2+y_1^2-r^2}$ *If the equation of the circle is $x^2+y^2+2gx+2fy+c=0,$ then the length of the tangent to the circle will be given by $PT=\sqrt{x_1^2+y_1^2+2g{x}_1+2f{y}_1+c}$ Length of intercepts made on axis by the tangent $x\mathrm{-intercept}=x_1\left[y_1/{\left(\frac{dy}{dx}\right)}_{\left(x_1,y_1\right)}\right]$
$y\mathrm{-intercept}=y_1-x_1{\left[\frac{dy}{dx}\right]}_{\left(x_1,y_1\right)}$