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CGP EDU Academic Team
Published on: August 12, 2026
Equations of circles which pass through the points (1, –2) and (3, – 4) and touch the x-axis is
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(b,c)Let equation of required circle is
x 2 + y 2 + 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 g 2 = c ⇒
g 2 – 2g – 15 = 0
g = 5, – 3
g = 5, c = 25, f = 10 ⇒ x 2 + y 2 + 10x + 20y + 25 = 0
g = –3, c = 9, f= 2 ⇒ x 2 + y 2 – 6x + 4y + 9 = 0
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