Comprehension A curve \( y=f(x) \) passes through the point \( P(1,1) \). The normal to the curv...

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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 equation of the curve \( y=f(x) \) is
(a) \( y=e^{a(x-1)} \)
(b) \( y=e^{a\left(x^{2}-1\right)} \)
(c) \( y=e^{a(1-|x|)} \)
(d) \( y=e^{a(|x|-1)} \)
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