Question

find the equation of the circum_circle of the triangle formed by the straight linnes given in each of the following. 2x+y=4, x+y=6, x+2y=5​

Answer 1

Answer:

x+y=6……………..(1)

2x+y=4……………….(2)

x+2y = 5………………..(3).

By solving the above equations the points of intersection of eqn.(1) and (2).

is A(-2,8) , eqn.(2)and (3) is B(1, 2) and eqn. (3) and(1) is C(7,-1).

Let the equation of a circle which passes thorough the points A , B and C is:-

x^2+y^2+2gx+2fy+c=0……………………..(4)

eqn. (4) passes thorough (-2 , 8) , (1,2) and (7, -1).

4+64–4g+16f+c=0. , or. -4g+16f+c=-68……………..(5)

1+4+2g+4f+c =0. , or. 2g+4f +c= -5…………………….(6).

49+1+14g-2f+c=0. or. 14g-2f +c = -50………………….(7)

By subtracting eqn.(6) from (5) and eqn.(7) from (6).

-6g+12f=-63. or. 2g-4f =21…………………..(8)

-12g+6f = 45. or. 4g-2f =-15………………….(9)

From eqn. (8) and (9).

g/(60+42)=f/(84+30) = -1/(-4+16)

g/102=f/114 =-1/12.

g=-17/2 , f = -19/2.

From eqn.(7).

-119+19+c=-50 => c= 100–50=50.

Required equation of the circle is:-

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