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  • The equation of the circle circumscribing the triangle whose sides are the lines y = x + 2, 3y = 4x, 2y = 3x is __________ .

The equation of the circle circumscribing the triangle whose sides are the lines y = x + 2, 3y = 4x, 2y = 3x is __________ .

Answers (1)

Given equation of line are y=x+2

3y=4x

2y=3x  

Solving these lines, we get points of intersection A(6,8), B (4,6) and C(0,0). 

 Let the equation of circle circumscribing the given triangle be

x2+y2+2gx+2fy+c=0

36+64+12g+16f+c=0⇒12g+16f+c=-100

16+36+8g+12f+c=0⇒8g+12f+c=-52

0+0+0+0+c=0⇒c=0

3g+4f=-25

2g+3f=-13

On solving we get g=-23 and f=11

The equation of circle is x2+y2-46x+22y=0

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