after an implicit differentiation of the circles equation we get:

thus the general equation of the slope of any tangent to the circle is:

the general equation of a line passing through a coordinate (a,b) with a slope m is:

the slope m can be obtained from:

thus the equation of the tangent is:

if we substitute (x,y) = (a,b) in the equation of the given circle we get:

thus the equation of the tangent is: