Comprehension Let \( C \) be a curve \( f(x, y)=0 \) passing through \( (1,1) \) such that it is...

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Comprehension
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 area enclosed by the curve \( C \) and its tangent at \( (1,1) \) and \( x \)-axis is equal to
(a) \( 1-\cot ^{-1} \sqrt{3} \)
(b) \( \tan ^{-1} \sqrt{3}-1 \)
(c) \( 1-\sec ^{-1} \sqrt{2} \)
(d) \( \sin ^{-1}(1)-1 \)
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