Question

Find the radius of the circle passing through the points (0,0), (-2,1)and (-3,2)

Answer 1

Answer:

Step-by-step explanation:

Let P(x, y) be the centre of the circle passing through the points O(0, 0), A(-2, 1) and B(-3, 2). Then,

OP = AP = BP

Now, OP = AP  OP2 = AP2

x2 + y2 = (x + 2)2 + (y - 1)2

x2 + y2 = x2 + y2 + 4x - 2y + 5

4x - 2y + 5 = 0 ...(i)

Now, OP = BP  OP2 = BP2

x2 + y2 = (x + 3)2 + (y - 2)2

x2 + y2 = x2 + y2 + 6x - 4y + 13

6x - 4y + 13 = 0 ...(ii)

On solving equations (i) and (ii), we get x = 3/2 and y =  11/2

Thus, the coordinates of the centre are ( 3/2 , 11/2)

Now, radius = OP = √(x^2+y^2) =√9/4 + 121/4 =1/2 √130