Answer :
Solution
Step 1:
The equation of an ellipse is
[tex]\frac{(x-h)^2}{a^2}\text{ + }\frac{(y-k)^2}{b^2}\text{ = 1}[/tex]where (h,k) is the center, a and b are the lengths of the semi-major and the semi-minor axes.
Step 2
Thus, h = 5, k=1, a = 1.
The following equation takes into account different properties of an ellipse:
[tex]\begin{gathered} \left(k+9\right)^2=b^2. \\ (1+9)^2=b^2 \\ 10^2\text{ = b}^2 \\ \text{b = 10} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} The\text{ }standard\text{ }form\text{ }is\text{ }\frac{\left(x - 5\right)^{2}}{1^{2}}+\frac{\left(y - 1\right)^{2}}{10^{2}}=1 \\ \\ or \\ \\ The\text{ }vertex\text{ }form\text{ }is\text{ }\left(x-5\right)^2+\frac{\left(y - 1\right)^{2}}{100}=1 \end{gathered}[/tex]