Advertisements
Advertisements
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
shaalaa.com
Is there an error in this question or solution?