Find the coordinates of the centre of the circle passing through the points (0, 0), (-2, 1),and (-3, 2). Also, find its radius.
Answers
Answer:
Centre ( 3/2, 11/2 )
Radius √130 / 2
Step-by-step explanation:
Let the centre be at ( a, b ) and let the radius be r.
Then the circle is given by
( x - a )² + ( y - b )² = r².
As ( 0, 0 ) is on the circle, we have
( 0 - a )² + ( 0 - b )² = r² => a² + b² = r² ... (1)
As ( -2, 1 ) is on the circle, we have
( -2 - a )² + ( 1 - b )² = r² => 4 + 4a + a² + 1 - 2b + b² = a² + b²
=> 4a - 2b + 5 = 0 ... (2)
As ( -3, 2 ) is on the circle, we have
( -3 - a )² + ( 2 - b )² = r² => 9 + 6a + a² + 4 - 4b + b² = a² + b²
=> 6a - 4b + 13 = 0 ... (3)
Subtracting twice equation (2) from equation (3) to eliminate b gives:
(6-8)a - (4-4)b + (13-10) = 0
=> -2a + 3 = 0
=> a = 3/2
Putting this into (2) gives
2b = 4a + 5 = 6 + 5 = 11 => b = 11/2
Using (1) gives
r² = a² + b² = (3/2)² + (11/2)² = 130/4 => r = √130 / 2