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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.
What is the Differential equation of circles tangent to x-axis?
[1+(y')2]3 = [yy"+1+(y')2]2
Are tangent circles two circles that are tangent to the same line at the same point?
Yes.
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.
Are circles tangent when they meet at a single point?
Yes, circles that share one and only one point are tangent to each other.
Can a line be tangent to one circle and a secant to the other in concentric circles?
Yes, it can as long as it is not the tangent line of the outermost circle. If it is tangent to any of the inner circles it will always cross the outer circles at two points--so it is their secant line--whereas the tangent of the outermost circle is secant to no circle because there are no more circles beyond that last one.
What are two coplanar circles that intersect at exactly one point?
Tangent circles.
A line that is tangent to two circles?
... touches each circle in exactly one point on each circle. given any two circles where none is entirely inside or inside and tangent to the other, there are at most four straight lines that are tangent to both circles.
The definition of external tanget?
An external tangent is a line that is tangent to both circles but does not pass between them.
