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Find the curve for which the perpendicul...

Find the curve for which the perpendicular from the foot of the ordinate to the tangent is of constant length.

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Find the cartesian equation of the curves for which the length of the tangent is of constant length.

Find the equation of the curve in which the perpendicular from the origin on any tangent is equal to the abscissa of the point of contact.

Knowledge Check

  • Find the co-ordinate of the foot of the perpendicular drawn form the origin to the plane 5y+8=0

    A
    `(0,(8)/(5),0)`
    B
    `(0,-(8)/(5),0)`
    C
    `(0,-(18)/(5),2)`
    D
    `((8)/(25),0,0)`

  • There is curve in which the length of the perpendicular from the orgin to tangent at any point is equal to abscissa of that point. Then,

    A
    `x^2+y^2=2` is one such curve
    B
    `y^2=4x` is one such curve
    C
    `x^2+y^2=2cx` (c parameters) are such curve
    D
    there are no such curves

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    The curve for which the ratio of the length of the segment intercepted by any tangent on the Y-axis to the length of the radius vector is constant (k), is

    Find the curve for which the sum of the lengths of the tangent and subtangent at any of its point is proportional to the product of the co-ordinates of the point of tangency, the proportionality factor is equal to k.

    The co-ordinates of foot of the perpendicular from the point (2,4) on the line x+y=1 are:

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