The equation of the ellipse in the standard form is written in the form,
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=[/tex]
Given:
[tex]\begin{gathered} Focus=(2,0),\text{ so c=2,c}^2=2^2=4 \\ Vertex=(5,0),\text{ so a=2,}a^2=5^2=25 \end{gathered}[/tex]
Therefore, let us evaluate for b^2
[tex]\begin{gathered} c^2=a^2-b^2 \\ 4=25-b^2 \\ b^2=25-4=21 \\ \therefore b^2=21 \end{gathered}[/tex]
Let us substitute the values of a^2=25, and b^2=21 into the standard form of the equation
[tex]\frac{x^2}{25}+\frac{y^2}{21}=1[/tex]
Hence, the answer is
[tex]\frac{x^2}{25}+\frac{y^2}{21}=1[/tex]
