Question

What is the equation of the line tangent to the circle at the given point x^2+y^2=20 at (-4,2)

Answer 1

`\bf x^2+y^2=20\implies 2x+2y\cfrac{dy}{dx}=0\implies x+y\cfrac{dy}{dx}=0\\\\\\ \cfrac{dy}{dx}=\cfrac{-x}{y}\\\\ -------------------------------\\\\ y'(-4,2)=\cfrac{-(-4)}{2}\implies y'(-4,2)=2\\\\ -------------------------------\\\\ y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=2(x-(-4)) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-2=2(x+4)\implies y-2=2x+8\implies \boxed{y=2x+10}`