This indicates that the tangents to the
curves at these points are parallel Thus, 
2
C
2
C
F ( )
x dx
x
x
=
+
=
∫
(say), implies that
292
MATHEMATICS
the tangents to all the curves y = F C (x), C ∈ R, at the points of intersection of the
curves by the line x = a, (a ∈ R), are parallel Further, the following equation (statement)
( )
F ( )
C
(say)
f x dx
x
y
=
+
=
∫
,
represents a family of curves The different values of C will correspond to different
members of this family and these members can be obtained by shifting any one of the
curves parallel to itself