Question

Hey !✌️

Find the equation of the circle whose centre is (2,-3) and which passes through the intersection of the lines 3x+2y=11 and 2x+3y=4.

Answer 1

The given lines are 3x + 2y = 11 and 2x + 3y = 4. Solving for x and y we get x = 5 and y = - 2. Hence the point of intersection is (5,-2). Therefore, the radius of the circle is equal to the distance between (2,-3) and (5,-2) which is √10 by distance formula.

Hence the equation of the circle is

(x-2)^2 + (y+3)^2 = 10