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Figure shows a circle that touches the y -axis at D and makes intercept AB at y-axis.

We are given that OD = 3 unit and AB = 8 unit .

Let C be the centre of circle and CE is perpendicular to chord AB .

Hence we get , AE = BE = 4 unit

CE = OD = 3 unit

Hence AC = 5 unit

Hence AC is radius of circle ,  DC= AC = 5 unit

Hence center coordinate of circle is C ( 5, 3 )

If center is (h, k ) and radius of circle is r , then equation of circle is

(x-h)² + ( y - k )² = r²

hence equation of circle that has centre at ( 5, 3 ) and radius 5 unit is

(x-5)² + (y - 3)² = 5²

Hence, equation of circle is  x² + y² -10x - 6y + 9 = 0