I am having some difficulty with my GCSE Maths homework for Year 11. The question reads "The line $L$ is a tangent to the circle $x^2 + y^2 = 80$ at the point $(-4, 8)$. Line $L$ crosses the $x$ axis at point $P$. Work out the coordinates of point P."
This question has completely stumped me, and I can't seem to find any help elsewhere online.
we compute the slope: $$2x+2yy'=0$$ from here we get $$y'=-\frac{x}{y}$$ for the Point $P(-4;8)$ we get $$y=\frac{1}{2}$$ thus our equation is given by $$y=\frac{1}{2}x+10$$ from the equation $$0=\frac{1}{2}x+10$$ we get $$x=-20$$