Find the locus of the center of the circle touching the circle `x^2+y^2-4y-2x=2sqrt3-1 Internally and tangents on which from (1, 2) are making of `60^0` with each other.

Find the locus of the center of the circle touching the circle x^2+y^2-4y=4 internally and tangents on which from (1, 2) are making of 60^0 with each other.

Find the equation of the family of circles touching the lines x^2-y^2+2y-1=0.

Find the equation of a circle with center (4, 3) touching the circle x^2+y^2=1

Find the locus of the centres of the circle which cut the circles x^2+y^2+4x-6y+9=0 and x^2+y^2-5x+4y-2=0 orthogonally

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

The locus of the point (h,k) for which the line hx+ky=1 touches the circle x^2+y^2=4

Find the locus of the midpoint of the chord of the circle x^2+y^2-2x-2y=0 , which makes an angle of 120^0 at the center.

Find the length of the tangent from (2,-3) to the circle x^(2) + y^(2) -8y -9y + 12=0

Consider the locus of center of the circle which touches the circle x^(2)+y^(2)=4 externally and the line x=4. The distance of the vertex of the locus from the otigin is __________ .

Find the equation of the circle whose radius is 5a n d which touches the circle x^2+y^2-2x-4y-20=0 externally at the point (5,5)dot