14. As shown in the figure, circle $C$ is tangent to the $x$-axis at point $T(1,0)$ and intersects the positive $y$-axis at two points $A$ and $B$ (with $B$ above $A$), and $|AB| = 2$. (I) The standard equation of circle $C$ is $\_\_\_\_$ ; (II) A line is drawn through point $A$ intersecting circle $O: x^2 + y^2 = 1$ at points $M$ and $N$. Consider the following three conclusions: (1) $\frac{|NA|}{|NB|} = \frac{|MA|}{|MB|}$ ; (2) $\frac{|NB|}{|NA|} - \frac{|MA|}{|MB|} = 2$ ; (3) $\frac{|NB|}{|NA|} + \frac{|MA|}{|MB|} = 2\sqrt{2}$ . The correct conclusion(s) is/are $\_\_\_\_$ . (Write the numbers of all correct conclusions) (B) Optional Questions (Choose one of questions 15 and 16 to answer. First fill in the box after the question number you choose on the answer sheet with a 2B pencil. If you choose both, only question 15 will be graded.)
14. As shown in the figure, circle $C$ is tangent to the $x$-axis at point $T(1,0)$ and intersects the positive $y$-axis at two points $A$ and $B$ (with $B$ above $A$), and $|AB| = 2$.\\
(I) The standard equation of circle $C$ is $\_\_\_\_$ ;\\
(II) A line is drawn through point $A$ intersecting circle $O: x^2 + y^2 = 1$ at points $M$ and $N$. Consider the following three conclusions:\\
(1) $\frac{|NA|}{|NB|} = \frac{|MA|}{|MB|}$ ;\\
(2) $\frac{|NB|}{|NA|} - \frac{|MA|}{|MB|} = 2$ ;\\
(3) $\frac{|NB|}{|NA|} + \frac{|MA|}{|MB|} = 2\sqrt{2}$ .
The correct conclusion(s) is/are $\_\_\_\_$ . (Write the numbers of all correct conclusions)\\
(B) Optional Questions (Choose one of questions 15 and 16 to answer. First fill in the box after the question number you choose on the answer sheet with a 2B pencil. If you choose both, only question 15 will be graded.)