Question

Graph the following. State the center and foci. (x-2)^2/9 + (y+1)^2/25 = 1

Answer 1

Case: Equation of Ellipse

`((x-h)^2)/(a^2)+((y-k)^2)/(b^2)=1`

Method:

a) Center

`\begin{gathered} ((x-2)^2)/(9)+((y+1)^2)/(25)=1 \\ The\text{ }Center\text{ }(h,k) \\ The\text{ }Center\text{ }is\text{ }(2,-1) \end{gathered}`

b) The foci

a= 3, b= 5

The foci is:

`\begin{gathered} (h,k+c),(h,k-c) \\ c=√(b^2-a^2) \\ c=√(5^2-3^2) \\ c=√(25-9) \\ c=√(16) \\ c=4 \\ Hence \\ (2,-1+4),(2,-1-4) \\ (2,3),(2,-5) \end{gathered}`

Final answer:

a) Center = (2, -1)

b) Foci= (2,3) and (2, -5)