JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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Application +4 | -1

A curve

y = f\left( x \right)

passes through the point

P\left( {1,1} \right)

. The normal to the curve at point

P

a\left( {y - 1} \right) + \left( {x - 1} \right) = 0

. If the slope of the tangent at any point on the curve is proportional to the ordinate at that point, then the equation of the curve is

View answer and explanation

Correct option: D

y = {e^{a\left( {x - 1} \right)}}

Option D (

y = {e^{a\left( {x - 1} \right)}}

) is correct because it satisfies the given conditions of passing through (1,1) and having a tangent slope proportional to the ordinate.

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