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A normal at any point (x , y) to the ...

A normal at any point `(x , y)` to the curve `y=f(x)` cuts a triangle of unit area with the axis, the differential equation of the curve is

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A normal at any point (x,y) to the curve y=f(x) cuts triangle of unit area with the axes,the equation of the curve is :

A curve y=f(x) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of the point P from the x-axis. Then the differential equation of the curve

Knowledge Check

  • A normal is drawn at a point P(x,y) of a curve. It meets the X-axis at Q. If PQ is of constant length k, then the differential equation describing such a curve is

    A
    `y (dy)/(dx) =+- sqrt(k^2-y^2)`
    B
    `y (dy)/(dx) =+- sqrt(k^2-x^2)`
    C
    `y (dy)/(dx) =+- sqrt(y^2-k^2)`
    D
    `x (dy)/(dx) =+- sqrt(x^2-k^2)`

  • A normal is drawn at a point P (x, y) of a curve. It meets the X- axis at Q. If PQ is of constant length k, then the differential equation describing such a curve is

    A
    `y dy/dx = +- sqrt (k^2-y^2)`
    B
    `x dy/dx = +- sqrt (k^2-x^2)`
    C
    `y dy/dx = +- sqrt (y^2-k^2)`
    D
    `x dy/dx = +- sqrt (x^2-k^2)`

  • If a curve is such that line joining origin to any point P (x,y) on the curve and the line parallel to y-axis through P are equally inclined to tangent to curve at P, then the differential equation of the curve is:

    A
    `x ((dy)/(dx))^2 -2y (dy)/(dx) =x `
    B
    `x ((dy)/(dx))^(2) +2y (dy)/(dx) =x `
    C
    `y ((dy)/(dx))^(2) -2x (dy)/(dx) =x `
    D
    `y ((dy)/(dx))^(2) -2y (dy)/(dx) =x `

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    If length of tangent at any point on the curve y=f(x) intercepted between the point and the x -axis is of length l. Find the equation of the curve.

    If length of tangent at any point on th curve y=f(x) intercepted between the point and the x -axis is of length 1. Find the equation of the curve.

    A normal is drawn at a point P(x,y) of a curve.It meets the x-axis at Q. If PQ has constant length k, then show that the differential equation describing such curves is y(dy)/(dx)=+-sqrt(k^(2)-y^(2)). Find the equation of such a curve passing through (0,k).

    At any point on the curve y=f(x) ,the sub-tangent, the ordinate of the point and the sub-normal are in

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