A circle touching the x-axis at (3,0) and making an intercept of length 8 on the y-axis passes through the point.

Correct option is A (3,10)
Equation of circles are (x−3)²+(y−5)²=25 (x−3)²+(y+5)²=25 ⟹x²+y²−6x+10y+9=0
The point on the circle will be (3, 2×5) = (3,10)