find tangent line to the circle x^2 + y^2=100 at point (-6,8)

Answer 1

using calculus,
2x + 2y dy/dx = 0
dy/dx = -x/y
at (-6,8) , dy/dx = slope = 6/8 = 3/4

non-calculus:
slope of radius from (0,0) to (-6,8)
= (8-0)/(-6-0) = -4/3
so slope of the the tangent, which has to be perpendicular, is +3/4

tangent equation:
y = (3/4)x + b
8 = (3/4)(-6) + b
b = 8+9/2 = 25/2

tangent: y = (3/4)x + 25/2
or 3x - 4y = -50