A circle is given by `x^2 + (y-1) ^2 = 1`, another circle C touches it externally and also the x-axis, then the locus of center is:

Let C_1 and C_2 be two circles with C_2 lying inside C_1 circle C lying inside C_1 touches C_1 internally andexternally. Identify the locus of the centre of C

A circle C_1 , of radius 2 touches both x -axis and y - axis. Another circle C_2 whose radius is greater than 2 touches circle and both the axes. Then the radius of circle is

If two circles (x+4)^(2)+y^(2)=1 and (x-4)^(2)+y^(2)=9 are touched extermally by a circle, then locus of centre of variable circle is

Find the equation of the circle which touches the x-axis and whose center is (1, 2).

The locus of the centres of circles which touches (y-1)^(2)+x^(2)=1 externally and also touches X-axis is

A circle C_1 of radius b touches the circle x^2 + y^2 =a^2 externally and has its centre on the positiveX-axis; another circle C_2 of radius c touches the circle C_1 , externally and has its centre on the positive x-axis. Given a lt b lt c then three circles have a common tangent if a,b,c are in

If C_1: x^2+y^2=(3+2sqrt(2))^2 is a circle and P A and P B are a pair of tangents on C_1, where P is any point on the director circle of C_1, then the radius of the smallest circle which touches c_1 externally and also the two tangents P A and P B is 2sqrt(3)-3 (b) 2sqrt(2)-1 2sqrt(2)-1 (d) 1

lf a circle C passing through (4,0) touches the circle x^2 + y^2 + 4x-6y-12 = 0 externally at a point (1, -1), then the radius of the circle C is :-

If a circle passes through the point (a, b) and cuts the circle x^2 +y^2=k^2 orthogonally, then the equation of the locus of its center is

The locus of the centres of the circles, which touch the circle, x^(2)+y^(2)=1 externally, also touch the Y-axis and lie in the first quadrant, is