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Find the equation of the curve in which ...

Find the equation of the curve in which the subnormal varies as the square of the ordinate.

Text Solution

Verified by Experts

The correct Answer is:
`y=ce^(kx)`
Since subnormal is `y(dy)/(dx)`
we have `y(dy)/(dx) = ky^(2)`
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Knowledge Check

  • An equation of the curve in which subnormal varies as the square of the ordinate is (k is constant of proportionally)

    A
    `y-Ae^(kx)`
    B
    `y=e^(kx)`
    C
    `y^2//2+kx=A`
    D
    `y^2+kx^2=A`

  • Equation of the curve in which the subnormal is twice the square of the ordinate is given by

    A
    `log y = 2x +log c`
    B
    `y=ce^(2x)`
    C
    `log y =2x^2 -log c`
    D
    None of these

  • The equation of the curve whose subnormal is twice the abscissa, is

    A
    a circle
    B
    a parabola
    C
    an ellipse
    D
    a hyperbola

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    Show that at any point on the hyperbola xy=c^(2), the subtangent varies as the abscissa and the subnormal varies as the cube of the ordinate of the point of contact.

    Find the equation of curves for which the cartesian subtangent varies as the abscissa.

    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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