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If the circle and x-axis are tangential then the centre of the circle must be at a distance equal to the radius away from the x-axis. That is, the centre of the circle must lie on y = ±r (where r = radius) so that the coordinates of the centre are (a, ±r)
So the equation of the set of circles is
(x - a)2 + (y ± r)2 = r2
Differentiating gives
2*(x - a) + 2*(y ± r)*dy/dx = 0
(x - a) + (y ± r)*dy/dx = 0
so that
dy/dx = (a - x)/(y ± r)
It is not clear why you would want the differential equation, but you asked for it so you've got it!
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What is the differential equation of the circle tangent to y axis?
dy/dx = (r - x)/sqrt(2xr - x2) , I hope!
What are tangent circles?
Tangent circles are circles that touch one another without crossing. The distance between the centres of the circles must be equal to the difference or the sum of their radii.
Do tangent circles have the same center?
No, tangent circles do not have the same center. They just touch at the side. Here is an example:
Can two circles be tangent at the same point?
If the two circles are tangent to each other,then it must be at the same point.
Can a tangent circle be concentric?
No; tangent circles touch each other at one point but concentric circles cannot not touch.
