How Can We Find The Angle Between Two Curves?

The angle between two curves at the point of intersection is the angle b/w their tangents:
Tan (theta) =m₂-m₁/ 1-m₁m₂   where m₁ and m₂ are the slopes
Y²=4ax   x²=4ay
x=y²/4ax
Put in x²=4ay
Y⁴/16a² =4ay
By solving we get;
y=0 and   y=4a
 
 
When   y=0   then x=0      we get (0, 0)
When   y=4a   then x=4a    we get (4a, 4a)
 
Y²=4ax
Differentiate it
2ydy/dx=4a
dy/dx=2a/y
 
at point (4a, 4a)
m₁=2a/4a=1/2
 
x²=4ay
y=1/4a x²
dy/dx= x/²a
at the point (4a, 4a)
m₂=4a/2a= 2
let theta be the angle b/w them
tan(theta)=m₂-m₁/1-m₁m₂
tan(theta)=3/4
theta=tan-1(3/2)
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