7 The two points \( (-2,4) \) and \( (1,3) \) lie on a circle \( x^{2}+y^{2}+a x+b y+c=0 \).
a Find two equations in \( a, b \), and \( c \), and solve the system of equations.
b Explain why infinitely many solutions are obtained in a.
c Suppose the point \( (4, q) \) also lies on the circle.
i Find the value of \( q \) for which the system of equations in \( a, b \), and \( c \) has no solutions. Explain this result geometrically.
ii Find the equation of the circle when \( q=12 \).