show that the follwoing curve intersect orthogonally at the indicated points 

x^2 = 4y and 4y + x^2 = 8 at (2,1)

We know that the two curve intersect orthogonally if angle between their tangents at the point of intersection is 90 degree & two tangents are perpendicular if product of their slope is -1.
(dy/dx)1 = 2x/4 = x/2 = 1
(dy/dx)2 = -2x/4 = -x/2 = -1
clearly product of slope is -1 hence curve intersect orthogonally.