Exercise 8.7 - Regularizing separate terms in 2d logistic regression

The decision boundary is given by:

hence a straight line in the $X_1-X_2$ plane.

For question (a), the decision boundary is an arbitrary line.

For question (b), the decision boundary is a line that passes the origin.

For question (c), the decision boundary is a line parallel to the $X_1$ axis.

For question (c), the decision boundary is a line parallel to the $X_2$ axis.