Coordinate of point $M(x,y)$ on the circle

Question

Let a point $M$ moving on the circle $(x-4)^2+(y-8)^2=20$ . If the point seperated out from the circle along tangent and intersect $x$ axis at point $(-2,0)$ . Then the point on the circle at where point $M$ seperated out from the circle is

Try: Let coordinate of point $M$ in parametric form is $\bigg(4+2\sqrt{5}\cos\theta, 8+2\sqrt{5}\sin \theta\bigg)$.

I did not understand how to go further, please help me , thanks

Answer 1

Let coordinates of that point be (x,y)

$\cfrac{y-8}{x-4} \cfrac{y-0}{x+2} = -1$
And use the fact that (x,y) lies on the circle $\implies (x-4)^2 + (y-8)^2 = 20$

Solve for x and y.