TANGENTS AND NORMALS

show that the following curve intersect orthogonally at the indicated points

x^2=y and x^3 + 6y = 7 at (1,1)

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 = 2
(dy/dx)2 = -3x²/6 = -1/2
Clearlly product of slope is -1 hence given curve intersect orthogonally.