Let centre of circle be C(α,β).
It lies in line y−4x+3−0⇒β=4α−3
∴C(α,4α−3)
∴CA=CB
By distance formula,
⇒(α−2)2+(4α−6)2=(α−4)2+(4α−8)2
⇒−4α+4−48α+36=−8α+16−64α+64
⇒(64+8−4−48)α=80−40
⇒α=2040=2
∴C(2,5)
∴r=(2−2)2+(5−3)2=2
A circle passes through the points (2,3) and (4,5). If its centre lies on the line y−4x+3=0, then its radius is equal to :
Held on 15 Apr 2018 · Verified 6 Jul 2026.
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