If at every point of a certain curve, the slope of the tangent equals $${{ - 2x} \over y}$$ the curve is

Let $${G_1}$$ and $${G_2}$$ be subgroups of a group $$G$$.
(a) Show that $${G_1}\, \cap \,{G_2}$$ is also a subgroup of $$G$$.
(b) $${\rm I}$$s $${G_1}\, \cup \,{G_2}$$ always a subgroup of $$G$$?

Prove that in a finite graph, the number of vertices of odd degree is always even.

How many minimum spanning tress does the following graph have? Draw them (Weights are assigned to the edges).