Given, equations of curves are
y2 = 4ax .....(i)
and x2 = 4by .....(ii)
Clearly, the angle of intersection of curves (i) and (ii) is the angle between the tangents to the curves at the point of intersection.
So, let us first find the intersection point of given curves.
On substituting the value of y from Eq. (ii) in Eq. (i), we get
Angle of intersection at (0, 0)
or Tangent to the curve (i) is parallel to Y-axis and tangent to the curve (ii) is parallel to X-axis.