Find an equation for the circle that goes through the points (0, 0), (0, 8), and (6, 12). Find an equation for the line that is tangent to this circle at (6, 12).
A circle has equation $\displaystyle $${x^2} + {y^2} + Ax + By + C = 0$$$ $\displaystyle $$A,B,C \in {\Cal R}$$$.
You have three points given and three unknown letters( A,B,C). Find them.
Then the equation of the tangent is $\displaystyle $$\left( {x - {x_0}} \right)\left( {{x_1} - {x_0}} \right) + \left( {y - {y_0}} \right)\left( {{y_1} - {y_0}} \right) =
{r^2}$$$
where x0,y0 is the center of the circle
x1,y1 the tangency point and r its radius