Question

Find the equation of the circum-circle of the triangle formed by the straight line given 2x + y = 4, x + y = 6, x + 2y = 5

Answer 1

Answer:

Step-by-step explanation:

Let the triangle be ABC.

Equation of AB: x+y=6         ... (i)

Equation of BC: 2x+y=4       ... (ii)

Equation of CA: x+2y=5       ... (iii)

 

Solve equations (i) and (ii) to get the vertices of B.

Solve equations (ii) and (iii) to get the vertices of C.

Solve equations (i) and (iii) to get the vertices of A.

 

Now, we need to find the equation of the circle passing through A, B and C.

 

Let the equation of the circle be x^2 + y^2 + 2gx + 2fy + c = 0           ... (A)

 

Substitute the value of x and y for each of the three coordinates in the above equation.

You will get three equations. Solve them to find f, g, c.