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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. Determine the equation of the curve. Also obtain the area bounded by the y-axis, the curve and the normal to the curve at `P`.

Answer

Step by step text solution for 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. Determine the equation of the curve. Also obtain the area bounded by the y-axis, the curve and the normal to the curve at P. by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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Knowledge Check

  • A curve y = f(x) passes through point P(1,1). The normal to curve at point P is a (y-1) + (x-1) = 0. If slope of tangent at any point on curve is proportional to ordinate at that point, then equation of curve is

    A
    `y = e^(ax) - 1`
    B
    `y = e^(ax) +1`
    C
    `y = e^(ax) + a`
    D
    `y = e^(a(x-1))`

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