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Let the circle cut the chord of length 4 on X-axis at point A and the chord of length 6 on the Y-axis at point B.
∴ the co-ordinates of point A are (4, 0) and co-ordinates of point B are (0, 6).
Since ∠BOA is a right angle.
AB represents the diameter of the circle.
The equation of a circle having (x1 , y1) and (x2, y2) as endpoints of diameter is given by (x – x1) (x – x2) + (y – y1) (y – y2) = 0
Here, x1 = 4, y1 = 0, x2 = 0, y2 = 6
∴ the required equation of the circle is
⇒ (x – 4) (x – 0) + (y – 0) (y – 6) = 0
⇒ x2 – 4x + y2 – 6y = 0
⇒ x2 + y2 – 4x – 6y = 0