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The point at which the circles x^(2)+y^(...

The point at which the circles `x^(2)+y^(2)-4x-4y+7=0 and x^(2)+y^(2)-12x-10y+45=0` touch each other is

A

`((13)/(5), (14)/(5))`

B

`((2)/(5),(5)/(6))`

C

`((14)/(5),((13)/(5))`

D

`((12)/(5), 2 + (sqrt(21))/(5))`

Text Solution

Verified by Experts

The correct Answer is:
C
Given circle are `S -= x^(2) + y^(2) - 4x - 4y + 7 = 0`
and `S^(1) -= x^(2) + y^(2) - 12 x - 10 y + 45 = 0`
Equation of common tangent 1s, `S = S^(1) = 0`
`implies 8x + 6y - 38 = 0`
`implies 4x + 3y - 19 = 0`
by verification, `((14)/(5), (13)/(5))` lies on equation (1)
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