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If circle C passing through the point (2...

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

A

`sqrt(12)`

B

`sqrt(13)`

C

`sqrt(15)`

D

4

Text Solution

Verified by Experts

The correct Answer is:
B

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`
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