Circle(s) touching x‑axis at a distance 3 from the origin and having an intercept of length 2 on y‑axis is(are)
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Let the equation of circle be

Put x = 0
⇒ y2 + y + 9 = 0
| y1 – y2 | =
⇒ ()2 – 36 = 28 ⇒ = 64 ⇒ = ± 8
So, equation of circles is x2 + y2 – 6x ± 8y + 9 = 0
Similarly, equation of other circle will be
x2 + y2 + 6x ± 8y + 9 = 0.
