Answer:

The intersection of the lines: 3x + 2y = 11 and 2x + 3y = 4 Is (5, – 2)

The general form of the equation of a circle is (x – h)² + (y – k)² = r²

(h, k) is the centre of the circle. r is the radius of the circle.

(h, k) = (2, – 3)

For determining the equation of the circle we need to determine the radius of the circle.

The circle passes through (5, – 2), that pair of values for x and y must satisfy the equation.

(5 – 2)² + ( – 2 – ( – 3))² = r²

3² + 1² = r²

r² = 9 + 1

∴ r² = 10

The equation of circle is,

(x – 2)² + (y – ( – 3))² = 10

(x – 2)² + (y + 3)² = 10