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Form the differential equation of family of circles having centre on y-axis and raduis 3 units -

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Question

Form the differential equation of family of circles having centre on y-axis and raduis 3 units

Options

  • `(x^2 - 9) ((dy^2)/(dx)) + x^2` = 0

  • `((dy^2)/(dx)) + x^2`

  • `(x^2 - 4) ((dy^2)/(dx)) + x^2` = 0

  • None of these

MCQ

Solution

`(x^2 - 9) ((dy^2)/(dx)) + x^2` = 0

Explanation:

Let the centre be [0, b]

∴ Equation of family of circles of raduis 3,

`x^2 + (y - b)^2` = 9 .......(1)  ......`[because r = 3]`

Differentiating w.r.t x

`2x + 2(y - b) y^1` = 0 or `y - b = - x/y^1`

Putting this value in (1)

`x^2 + (- x/y^1)^2` = 9 or `x^2y^12 + x^2 = 9y^2`

or `(x^2 - 9) y^12 + x^2` = 0

∴ Differential equation is `(x^2 - 9) ((dy)/(dx))^2 + x^2` = 0

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