Determine the equation of the line tangent to the circle at (-4, 7).
Determine the equation of a line that is perpendicular to the tangent line in part a) [-4,7] and tangent to the circle.
for a circle
x^2 + y^2 = r^2
dy/dx = -x/y
so at (-4,7) the slope is 4/7 and that makes the line
y-7 = 4/7 (x+4)
any line perpendicular to the tangent would have slope -7/4, so if we want that to be tangent to the circle, it would have to go through (7,4) or (-7,-4) -- now write that equation.