Given equation of the curves are, x2=8y....(1) xy=8....(2) On solving equation (1) and (2), we get x=4 y=2 Therefore, the point of intersection of given curves is (4,2). Slope of tangent to the curve (1) at point (4,2) is calculated as x2=8y 2x=8
dy
dx
⇒
dy
dy
=
x
4
⇒m1=1 Slope of tangent to the curve ( 2 ) at point (4,2) is calculated as xy=8 x
dy
dx
+y=0⇒
dy
dx
=−
y
x
⇒m2=−
1
2
The angle θ between the curves is calculated as, tanθ=(