Find the equation of the circle which passes through the points (1, 3)

1.	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: x² + y² + 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 x² + y² - 3x - 2y - 1 = 0

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: x² + y² + 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 x² + y² - 3x - 2y - 1 = 0

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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.

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