Question

find the equation of the circle circumscribing the Triangle formed by the lines x+y=6,2x+y=4 and x+2y=5

Answer 1

Solving the given equation of the lines which form the sides of the triangle in pairs, the coordinates of the vertices of a triangle obtained are : (-2, 8), (1, 2) and (7, -1).

The equation of the circle be,

x2 + y2 + 2gx + 2fy + c = 0  ……………..(i)

Substituting the co-ordinates of the vertices obtained in equation (i), we get

-4g + 16f + c = -68  …………………..(ii)

2g + 4f + c =-5  …………………..(iii)

14g – 2f  + c = -50 …………………(iv)

By solving the equations (i), (ii) and (iii), we get

g= -17/2  ;  f = -19/2  and c = 50.

Now substituting the values of g, f and c in equation (i), we get

x2 + y2 – 17x – 19y + 50  = 0, which is the required equation of the circle.

this answer is correct and the previous answer is wrong (refer to RS agarwal class 11 chapter 21 ,circles, exercise 21 B, question no. 16)

Answer 2

The required equation of circle be x^+y^-7x-19y+50=0