A circle has equation $$x ^ { 2 } + a x + y ^ { 2 } + b y + c = 0$$ where $a , b$ and $c$ are non-zero real constants. Which one of the following is a necessary and sufficient condition for the circle to be tangent to the $y$-axis? A $a ^ { 2 } = 4 c$ B $b ^ { 2 } = 4 c$ C $\frac { a } { 2 } = \sqrt { \frac { a ^ { 2 } + b ^ { 2 } } { 4 } - c }$ D $\frac { b } { 2 } = \sqrt { \frac { a ^ { 2 } + b ^ { 2 } } { 4 } - c }$ $\mathbf { E } \quad - \frac { a } { 2 } = \sqrt { \frac { a ^ { 2 } + b ^ { 2 } } { 4 } - c }$ $\mathbf { F } \quad - \frac { b } { 2 } = \sqrt { \frac { a ^ { 2 } + b ^ { 2 } } { 4 } - c }$
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A circle has equation
$$x ^ { 2 } + a x + y ^ { 2 } + b y + c = 0$$
where $a , b$ and $c$ are non-zero real constants.\\
Which one of the following is a necessary and sufficient condition for the circle to be tangent to the $y$-axis?
A $a ^ { 2 } = 4 c$\\
B $b ^ { 2 } = 4 c$\\
C $\frac { a } { 2 } = \sqrt { \frac { a ^ { 2 } + b ^ { 2 } } { 4 } - c }$\\
D $\frac { b } { 2 } = \sqrt { \frac { a ^ { 2 } + b ^ { 2 } } { 4 } - c }$\\
$\mathbf { E } \quad - \frac { a } { 2 } = \sqrt { \frac { a ^ { 2 } + b ^ { 2 } } { 4 } - c }$\\
$\mathbf { F } \quad - \frac { b } { 2 } = \sqrt { \frac { a ^ { 2 } + b ^ { 2 } } { 4 } - c }$