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Find the orthogonal trajectory of y^2=4a...

Find the orthogonal trajectory of `y^2=4a x` (a being the parameter).

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Find the orthogonal trajectories of xy=c

Find the orthogonal trajectories of xy=c

Knowledge Check

  • STATEMENT-1 : The orthogonal trajectory of a family of circles touching x-axis at origin and whose centre the on y-axis is self orthogonal. and STATEMENT-2 : In order to find the orthogonal trajectory of a family of curves we put -(dx)/(dy) in place of (dy)/(dx) in the differential equation of the given family of curves.

    A
    Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
    B
    Statement-1 is true, Statement-2 is true, Statement-2 is NOT a correct explanation for Statement-1.
    C
    Statement-1 is True, Statement-2 is False
    D
    Statement-1 is False, Statement-2 is True

  • Any curve which cuts every member of a given family of curve is called an orthogonal trajectory of family. To get this, we replace (dy)/(dx)by -(dx)/(dy) in differential equation. The orthogonal trajectories for y=ce^(-x) represent

    A
    exponential curves
    B
    family of ellipses
    C
    family of circle
    D
    family of parabolas

  • Any curve which cuts every member of a given family of curve is called an orthogonal trajectory of family. To get this, we replace (dy)/(dx) by -(dx)/(dy) in differential equation. The orthogonal trajectories for y=cx^(2) , where c is a constant is

    A
    a family of circles
    B
    family of straight lines
    C
    family of ellipses
    D
    family of hyperbolas

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    If (2,4) is a point on the orthogonal trajectory of x^2+y^2-ay=0 , then the orthagonal trajectory is a circle with diameter.

    If (2, 4) is a point on the orthogonal to trajectory of x^(2) + y^(2) - ay = 0 , then the orthogonl trajectory is a circle with radius__________

    If the orthogonal trajectory of y=ax^(2) where a is arbitrary constant) is y^(lambda_(1))=-(x^(lambda_(2)))/2+C (where C is arbitrary constant).Then lambda_(1)+lambda_(2) is

    Find the differential equation satisfied by family of parabolas y^(2)=4a(x+a) and show that the orthogonal trajectory of the system belongs to system itself.

    Find the orthogonal trajectories of family of curves x^(2)+y^(2)=cx

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