Question

Find the equation of a circle passing through three given points (1, 0),(0,0) and (0, 1).​

Answer 1

Answer:

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Step-by-step explanation:

Let the equation of the general form of the required circle be x2 + y2 + 2gx + 2fy + c = 0 ……………. (i)

According to the problem, the above equation of the circle passes through the points (1, 0), (-1, 0) and (0, 1). Therefore,

1 + 2g + c = 0 ……………. (ii)

1 - 2g + c = 0 ……………. (iii)

1 + 2f + c = 0 ……………. (iv)

Subtracting (iii) form (i), we get 4g = 0 ⇒ g = 0.

Putting g = 0 in (ii), we obtain c = -1. Now putting c = -1 in (iv), we get f = 0.

Substituting the values of g, f and c in (i), we obtain the equation of the required circle as x2 + y2 = 1.