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
Answers
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.