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(12)`
B. `sqrt(13)`
C. `sqrt(15)`
D. 4

Answer

B

Explanation

Tangent at (1,1) to ` x^2 +y^2 + 4x - 6y = 0`
` x + y + 2 (x+1) - 3 (y+1) = 0`
` 3 x - 2y -1 = 0`
` S + lamda L = 0` (Family of circle)
`x^2 + y^2 + 4 x -6y + lamda (3x - 2y - 1) = 0`
Passes (2,2)
` 4+ lamda = 0`
` lamda = - 4`
Equation of circle : ` x^2 + y^2 - 8 x + 2y + 4 = 0`
radius ` = sqrt(16 +1 - 4) = sqrt13`