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

Options

A. `sqrt(57)`
B. `2sqrt5`
C. 5
D. 4

Answer

C

Explanation

`S=x^(2)+y^(2)+4x-6y-12`
Tangent at (1, -1)
`x-y+2(x+1)-3(y-1)=12`
`3x-4y=7`
Family of such circles , `S+lamdaL=0`
`x^(2)+y^(2)+4x-6y-12+lamda(3x-4y-7)=0`
`16+16-12+lamda(12-7)=0`
`lamda=(-20)/5=-4`
Equation of circle : `x^(2)+y^(2)-8x+10y+16=0`
Radius = 5