Find the angle of intersection of the circles x^2-4x+y^2=0 and x^2+y^2=8

Answer 1

45 or 135 degrees

or pi/4 and 3pi/4 radians

solve each for y, and find the points of intersection, (2,2) and (2,-2)

the larger circle has slope of the tangent lines at those points of 1 and -1, which is a 45 or 135 degree angle with the horizontal. the smaller circle has tangent lines at the two points of 0. They're horizontal lines, y=2 and y=-2. (2,2) is the top of the smaller circle and (2,-2) is the bottom point of the smaller circle.

Graph the 2 circles to visualize it better. larger circle has center of the origin with radius 2sqr2

smaller circle has center at (2,0) with radius = 2