The locus of the centre of a circle touching the circle `x^2 + y^2 - 4y -2x = 2sqrt3 - 1` internally and tangents on which from (1,2) is making a `60^@` angle with each other is a circle. then integral part of its radius is

The locus of the centre of a circle touching the circle `x^2 + y^2 - 4

1.	The locus of the centre of a circle touching the circle `x^2 + y^2 - 4y -2x = 2sqrt3 - 1` internally and tangents on which from (1,2) is making a `60^@` angle with each other is a circle. then integral part of its radius is
Answer» `x^2+y^2-4y-2x=2sqrt3-1` `(x-1)^2+(y-2)^2=1+4+2sqrt3-1` `(x-1)^2+(y-2)^2=(sqrt3+1)^2` `C_1C_2=r_1+r_2` `(h-1)^2+(k-2)^2=(sqrt3+1+r)^2` `sin30^0=r/(sqrt3+1+r)` `sqrt3+1+r=2r` `r=sqrt3+1=2.732` 2 Answer

The slope of line which belongs to family (1+ l) x + (1-l)y + 2(1-l) = 0 and makes shortest intercept on `x^2 = 4y - 4`
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