The order and degree of the differential equation of the family of the circles touching the x-axis at the origin, are respectively:
A
1,1
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B
1,2
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C
2,1
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D
2,2
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Solution
The correct option is A1,1 The system of circles touching x-axis at origin will have centres on y-axis.
Let (0,a) be the centre of a circle.
Then the radius of the circle should be a units, since the circle should touch x-axis at origin. Equation of a circle with centre at (0,a) and radius a is (x−0)2+(y−a)2=a2 ⇒x2+y2−2ay=0 The above equation represents the family of circles touching x-axis at origin. Here 'a' is an arbitrary constant. In order to find the differential equation of system of circles touching x-axis at origin, eliminate the the arbitrary constant from equation Differentiating equation with respect to y, 2xdxdy+2y−2a=0 dxdy=2(y−a) ⇒ Order is 1 and degree is also 1. Hence, option 'A' is correct.