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

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

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SOLUTION:

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)

User Raveturned
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