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. $x^2+y^2-17x+19y+50=0$

Hint:

General circle equation: $x^2+y^2+2gx+2fy+c=0$.

Answer 1

The Correct Option is C

Step 1: Find vertices: Intersection of $x+y=6$ and $2x+y=4$ gives $x=-2,y=8$. Intersection of $x+y=6$ and $x+2y=5$ gives $x=7,y=-1$. Intersection of $2x+y=4$ and $x+2y=5$ gives $x=1,y=2$.}
Step 2: Circle through these points has equation $x^2+y^2+17x-19y-50=0$.}