SOLUTION:
Case: Equation of Ellipse
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
Method:
a) Center
[tex]\begin{gathered} \frac{(x-2)^2}{9}+\frac{(y+1)^2}{25}=1 \\ The\text{ }Center\text{ }(h,k) \\ The\text{ }Center\text{ }is\text{ }(2,-1) \end{gathered}[/tex]
b) The foci
a= 3, b= 5
The foci is:
[tex]\begin{gathered} (h,k+c),(h,k-c) \\ c=\sqrt{b^2-a^2} \\ c=\sqrt{5^2-3^2} \\ c=\sqrt{25-9} \\ c=\sqrt{16} \\ c=4 \\ Hence \\ (2,-1+4),(2,-1-4) \\ (2,3),(2,-5) \end{gathered}[/tex]
Final answer:
a) Center = (2, -1)
b) Foci= (2,3) and (2, -5)
