Book: Mathematics Part-II
Chapter: 9. Differential Equations
Subject: Maths - Class 12th
Q. No. 10 of Exercise 9.3
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Form the differential equation of the family of circles having centre on y-axis and radius 3 units.
Let the centre of the circle on y – axis be (0,b).
We know that the differential equation of the family of circles with centre at (0, b) and radius 3 is: x2 + (y- b)2 = 32
⇒ x2 + (y- b)2 = 9 ----(1)
Now, differentiating both sides w.r.t. x, we get,
2x + 2(y – b).y’ = 0
⇒ (y – b). y’ = x
⇒ y – b = 
Thus, substituting the value of ( y – b) in equation (1), we get,
⇒ x2((y’)2 + 1) = 9(y’)2
⇒ (x2 – 9)(y’)2 + x2 = 0
Therefore, the required differential equation is (x2 – 9)(y’)2 + x2 = 0
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