# Find the equation

The general equation of a circle: (x - h)2 + (y - k)2 = r2

…(i), where (h, k) is the centre and r is the radius.

Putting A(1, 1) in (i)

(1 - h)2 + (1 - k)2 = 12 h2 + k2 + 2 - 2h - 2k = 1 h2 + k2 - 2h - 2k = - 1..(ii)

Putting B(2, 2) in (i)

(2 - h)2 + (2 - k)2 = 12 h2 + k2 + 8 - 4h - 4k = 1 h2 + k2 - 4h - 4k = - 7 (h2 + k2 - 2h - 2k) - 2h - 2k = - 7 - 1 - 2h - 2k = - 7 [from (ii)] - 2h - 2k = - 6 h + k = 3 h= 3 - k

Putting it in (ii) (3 - k)2 + k2 - 2(3 - k) - 2k = - 1 9 + 2k2 - 6k - 6 + 2k - 2k = - 1 2k2 + 4 - 6k = 0 k2 - 3k + 2 = 0 k = 2 or k = 1

When k = 2, h = 3 - 2 = 1

Equation of 1 circle

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

When k = 1, h = 3 - 1 = 2

(x - 2)2 + (y - 1)2 = 1 Rate this question :

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