Comprehension \( \quad \) Let \( C \) be a curve \( f(x, y)=0 \) passing through \( (1,1) \) suc...

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Comprehension \( \quad \) Let \( C \) be a curve \( f(x, y)=0 \) passing through \( (1,1) \) such that it is orthogonal to family of circles \( x^{2}+y^{2}-a x=0 \), where \( a \) being parameter.
The shortest distance between the curve \( C \) and the parabola \( x^{2}=2 y+1 \) is equal to
(a) \( \sqrt{2}-1 \)
(b) \( \sqrt{2}+1 \)
(c) \( \sqrt{6}-1 \)
(d) \( \sqrt{5}-1 \)
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