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Find the equation of the curve which is such that the area of the rectangle constructed on the abscissa of any point and the intercept of the tangent at this point on the y-axis is equal to 4.

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Find the equation of the curve which is such that the area of the rectangle constructed on the abscissa of and the initial ordinate of the tangent at this point is a constanta =a^(2)

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Knowledge Check

  • The equation of the curve such that the subtangent at any point of the curve is two times the abscissa of the point and curve passes through point (1,2) is:

    A
    `y^(2) = x + 3`
    B
    `y = x^(2)`
    C
    `y^(2) = 4x`
    D
    `y = 2x^(2)`

  • The curve such that the ratio of the subnormal at any point to the sum of its abscissa and ordinate is equal to the ratio of the ordinate of this point to its abscissa is

    A
    `y=log|Cx|`
    B
    `y=x^2+Cx`
    C
    `y=xlogC(x^2+y^2)`
    D
    `y=xlog|Cx|`

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    The equation of the curve which is such that the portion of the axis of x cut off between the origin and tangent at any point is proportional to the ordinate of that point is

    Find the curve such that the area of the trapezium formed by the co-ordinate axes, ordinate of an arbitrary point & the tangent at this point equals half the square of its abscissa.

    The equation of the curve which is such that the portion of the axis of x cut-off between the origin and tangent at any point is proportional to the ordinate of that point is

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    The abscissa of any point on the y-axis is _____________

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