(A) What Can You Conclude About the Graph of the Solution

Essay

(a) What can you conclude about the graph of the solution of the equation $\frac { d y } { d x } = - \frac { x } { y }$ just by looking at the differential equation?
(b) Use implicit differentiation to verify all members of the family $x ^ { 2 } + y ^ { 2 } = c ^ { 2 }$ are solutions of the equation in part (a).(c) Find a solution of the equation in part (a) with the additional condition that $y ( 3 ) = 4$ .