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A curve y=f(x) passes through the point ...

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 ordinate of the point, find the equation of the curve.

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The correct Answer is:
`log y=a(x-1)`
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