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The differential equation of the family ...

The differential equation of the family of circles passing through the origin and having centres on the x-axis is

A

`x^2 = y^2 + xy dy/dx`

B

`x^2 = y^2 + 3xy dy/dx`

C

`y^2 = x^2 + 2xy dy/dx`

D

`y^2 = x^2 - 2xy dy/dx`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • The differential equation of all circles passing through the origin and having their centres on the x-axis is

    A
    `x^2=y^2+xy(dy)/(dx)`
    B
    `x^2=y^2+3xy(dy)/(dx)`
    C
    `y^2=x^2+2xy(dy)/(dx)`
    D
    `y^2=x^2-2xy(dy)/(dx)`

  • The differential equation of all circles passing through the origin and having their centres on the x-axis is :

    A
    `x^(2)-y^(2)+xy(dy)/(dx)`
    B
    `x^(2)=y^(2)+3xy (dy)/(dx)`
    C
    `y^(2)=x^(2)+2xy(dy)/(dx)`
    D
    `y^(2)=x^(2)-2xy(dy)/(dx)`

  • The differential equation of the family of circles passing through the fixed points (a,0) and (-a,0) is

    A
    `y_1(y^2-x^2)+2xy+a^2=0`
    B
    `y_1y^2+xy+a^2x^2=0`
    C
    `y_1(y^2-x^2+a^2)+2xy=0`
    D
    `y_1(y^2+x^2)-2xy+a^2=0`

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    The differential equation of the family of circles of fixed radius r and having their centres on y -axis is:

    The differential equation of all circles which pass through the origin and whose centres lie on y-axis is

    The differential equation of the family of circles passing through the fixed points (a, 0) and (-a, 0) is

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