Question

The equation of the circle circumscribing the triangle formed by the lines $ x+y=6, $ $ 2x+y=4 $ and $ x+2y=5 $ is:

• A. $ {{x}^{2}}+{{y}^{2}}+17x+19y-50=0 $
• B. $ {{x}^{2}}+{{y}^{2}}-17x-19y-50=0 $
• C. $ {{x}^{2}}+{{y}^{2}}+17x-19y-50=0 $
• D. $ {{x}^{2}}+{{y}^{2}}-17x+19y+50=0 $
• E. $ {{x}^{2}}+{{y}^{2}}-17x\,+19y+50=0 $

Answer 1

Answer: (D)

Lines, $ x+y=6,2x+y=4 $ and $ x+2y=5 $ Intersect at points $ (-2,8),(7-1) $ and (1, 2) Now, all these points lie on $ {{x}^{2}}+{{y}^{2}}-17x-19y+50=0 $ .