I'm assuming you have. The first thing we do is find the slope of the tangent line by finding the derivative of the equation at the point (5,6).
expanding the equation
x^2 - 4x + 4 + y^2 - 4y + 4 = 25
Finding the derivative
2x - 4 + 2y y' - 4y' = 0
y'( 2y - 4) = 4 - 2x
y' = (4 - 2x) / (2y - 4)
at the point (5,6) the slope = y' = (4 - 10) / (12 - 4) = -3/4
So the equation of tangent line is y - 6 = -3/4( x - 5)
y = -3/4x + 39/4
so the y intercept = =3/4(0) + 39/4 = 39/4 Answer
and x intercept = -39/4 / - 3/4 = 13 Answer
