Answer
$\frac{(x-1)^2}{10}+\frac{(y-2)^2}{1}=1$
See graph.
Work Step by Step
1. Given center $(1,2)$, focus $(4,2)$ and contain point $(1,3)$, we can identify a horizontal major axis, $c=4-1=3$, $a^2=b^2+c^2=b^2+9$
2. Write the equation as $\frac{(x-1)^2}{a^2}+\frac{(y-2)^2}{b^2}=1$, use the point on curve to get $\frac{(1-1)^2}{a^2}+\frac{(3-2)^2}{b^2}=1$, thus $b=1$ and $a^2=10$
3. Thus we have $\frac{(x-1)^2}{10}+\frac{(y-2)^2}{1}=1$
4. See graph.
