For both families, the lowest value of
p
i
for which the curve cuts the positive
x
-axis is 0. [For negative values of
p
i
the curves cut the negative
x
-axis.] Thecommon slope of the first family is
−
2 and for the second family it is
−
1. Thetwo lines with these slopes that pass through the origin determine the limit of theregion of validity of the solution (both constraints must be satisfied). In terms of the conventional angle
θ
measured from the positive
x
-axis,
−
14
π < θ <
12
π
+
φ
,