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Comprehension
A curve \( y=f(x) \) passes through the point \( P(1,1) \). The normal to the curve at \( P \) is \( a(y-1)+(x-1)=0 \). If the slope of the tangent at any point on the curve is proportional to the ordinates of the point, then
The area bounded by the curve \( y=f(x), y \)-axis and the normal to the curve at \( P \) is
(a) \( \frac{1}{a}\left(a-\frac{1}{2}+e^{-a}\right) \)
(b) \( \frac{1}{a}\left(a+\frac{1}{2}+e^{-a}\right) \)
(c) \( \frac{1}{a}\left(a-\frac{1}{2}+e^{a}\right) \)
(d) \( \frac{1}{a}\left(a+\frac{1}{2}+e^{a}\right) \)
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