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A circle touching the $x$-axis at $(3, 0)$ and making an intercept of length 8 on the $y$-axis passes through the point:
(1) $(3, 10)$
(2) $(3, 5)$
(3) $(2, 3)$
(4) $(1, 5)$
Circle: $(x-3)^2 + (y-k)^2 = k^2$. $y$-intercept $= 2\sqrt{k^2 - 9} = 8 \Rightarrow k^2 = 25$, $k = 5$. Circle: $(x-3)^2 + (y-5)^2 = 25$. $(3,10)$: $0 + 25 = 25$. Verified.
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