Question

Find the equation of the circle through the points (1, 0), (– 1, 0) and (0, 1)

Answer 1

Let the general equation of the circle be

x² + y² + 2gx + 2fy + c = 0

It passes through the points (1, 0), (– 1, 0) and (0, 1)

1 + 0 + 2g + c = 0

2g + c = – 1 .......(1)

1 + 0 – 2g + c = 0

– 2g + c = – 1 .......(2)

0 + 1 + 0 + 2f + c = 0

2f + c = – 1

(1) + (2)

⇒ 2c = – 2

c = – 1

Substitute in equation (1)

2g – 1 = – 1

2g = 0

g = 0

Substitute in equation (3)

2f – 1 = – 1

2f = – 1 + 1

2f = 0

f = 0

Therefore, the required equation of the circle

x² + y² – 1 = 0