Q. 103.7( 15 Votes )

# Find the equation of the circle which passes through the points (1, 3) and (2, - 1), and has its centre on the line 2x + y – 4 = 0.

Answer :

The equation of a circle:

x^{2} + y^{2} + 2gx + 2fy + c = 0…(i)

Putting (1, 3) & (2, - 1)in (i)

2g + 6f + c = - 10..(ii)

4g - 2f + c = - 5..(iii)

Since the centre lies on the given straight line, ( - g, - f) must satisfy the equation as

- 2g –f - 4 = 0…(iv)

Solving, f = - 1, g = - 1.5, c = - 1

The equation is

x^{2} + y^{2} - 3x - 2y - 1 = 0

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