(a) The equation of the tangent line can be written as
.. 3(x +6) -4(y -8) = 0
.. 3x -4y = -50
.. y = (3/4)x +25/2 . . . the equation of the tangent line
(b) The point of tangency will be the intersection of the circle with the perpendicular line through the circle center, y = (-1/5)x. A graphing calculator shows that point to be
.. (9.81, -1.96)
.. 3(x +6) -4(y -8) = 0
.. 3x -4y = -50
.. y = (3/4)x +25/2 . . . the equation of the tangent line
(b) The point of tangency will be the intersection of the circle with the perpendicular line through the circle center, y = (-1/5)x. A graphing calculator shows that point to be
.. (9.81, -1.96)