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 A circle C lying inside C_1 touches C_1 internally and C_2 externally. Identify the locus of the centre of C

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).

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?

A circle is drawn to cut a chord of length 2a unit along x-axis and to touch the y-axis. Then the locus of the centre of the circle is-

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 (a) 2sqrt(3)-3 (b) 2sqrt(2)-1 (c) 2sqrt(2)-1 (d) 1

Show that the circles x^(2) + y^(2) + 6x + 14y + 9 = 0 and x^(2) + y^(2) - 4x - 10y - 7 = 0 touch each other externally, find also the equation of the common tangent of the two circles.

Let be the circle with centre at (1 , 1) and radius is 1 unit . It T is the circle centred at (0 , y) , passing through origin and touching the circle c externally , then the radius of T is equal to _

If the chord of contact of tangents from a point (x_1,y_1) to the circle x^2+y^2=a^2 touches the circle (x-a)^2+y^2=a^2 , then the locus of (x_1,y_1) is :

If one end of the diameter is (1, 1) and the other end lies on the line x+y=3 , then find the locus of the center of the circle.