Question

# Find the equation of the circle which circumscribes the triangle formed by the lines x=0,y=0 and 2x+3y=6.

A
x2+y2+4x4y+3=0
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B
3x2+3y24x+6y=0
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C
3x2+3y2+4x4y=0
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D
3x2+3y24x+4y=0
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Solution

## The correct option is B 3x2+3y2−4x+6y=0Since the circle circumscribes the triangle, the three corners of the triangle are points on the circle. Find the points of intersection of the three lines.(0,0),(0,2),(3,0)eq of a circle is(x−a)2+(y−b)2=r2plug in the pointssolve 3 equations for 3 unknowns (a b and r)plug those back into the eq of a circle(0−a)2+(0−b)2=r2a2+b2=r2(0−a)2+(2−b)2=r2a2+b2−4b−4=r2 [since a2+b2=r2, −4b−4=0, or b=−1](3−a)2+(0−b)2=r29−6a+a2+b2=r2 [again since a2+b2=r2, 9−6a=0 or a=2/3]solve for r2(2/3)2+(−1)2=r213/9=r2so circle eq is (x−a)2+(y−b)2=r2(x−2/3)2+(y+1)2=139x2−43x+4/9+y2+2y+1=139x2−43x+y2+2y=03x2−4x+3y2+6y=0

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