Question

Let equation of required circle is

x² + y² + 2gx + 2fy + c = 0

it passes through (1, _2) & (3, _4)

2g _ 4f + c = _5

6g _ 8f + c = _25

4g _ 8f + 2c = _10

6g _ 8f + c = _25

_2g + c = 15

circle touches x-axis g² = c Þ

g² _ 2g _ 15 = 0

g = 5, _ 3

g = 5, c = 25, f = 10 Þ x² + y² + 10x + 20y + 25 = 0

g = _3, c = 9, f= 2 Þ x² + y² _ 6x + 4y + 9 = 0

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