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The differential equation of the family ...

The differential equation of the family of circles with fixed radius 5 units and centre on the line y=2 is

A

`(x-2)^(2)y'^(2)=25-(y-2)^(2)`

B

`(x-2)y'^(2)=25-(y-2)^(2)`

C

`(y-2)y'^(2)=25-(y-2)^(2)`

D

`(y-2)^(2)y'^(2)=25-(y-2)^(2)`.

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • The differential equation of family of circles whose centre lies on x-axis, is

    A
    `(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)+1=0`
    B
    `y(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)-1=0`
    C
    `y(d^(2)y)/(dx^(2))-((dy)/(dx))^(2)-1=0`
    D
    `y(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)+1=0`

  • The differential equation satisfied by all the circles with radius = r(constant) and center on the line x=y is

    A
    `(x-y)^2 (1+y_(1) ^2)= r^2 (1 + y_(1))^(2)`
    B
    `(x-y) y_(1)=r^2 (1 + y_(1)) (1 + y_(1))^(2)`
    C
    `(x-y) y_(1)^(2) =r^2 (1 + y_(1)^(2))y_(2)`
    D
    `(x-y) y_(1)^(2)= r^2(1 + y_(1))y_(2)^(2)`

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

    A
    ` 2xy (dy)/(dx) = x^(2) -y^(2)`
    B
    `2xy(dy)/(dx)= y^(2)-x^(2)`
    C
    ` 2xy (dy)/(dx) =x^(2)+y^(2)`
    D
    `2xy(dy)/(dx) +x^(2) +y^(2)=0`

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