Question

What are the coordinates of the four vertices and the two foci?

Answer 1

`\begin{gathered} ((x-2)^2)/(36)+((y+1)^2)/(25)=1 \\ \text{Foci} \\ F1\text{ (}h+c,k\text{)} \\ F2(h-c,k) \\ (h,k)=(2,-1) \\ c=\sqrt[]{a^2-b^2} \\ \text{from the equation} \\ a^2=36 \\ b^2=25 \\ c=√(36-25) \\ c=√(11) \\ Foci\text{ 1= (2}+√(11),-1) \\ Foci\text{ 2= (2-}\sqrt[]{11},-1) \\ \text{Vertices } \\ V1=(h+a,k) \\ V2=(h-a,k) \\ V1=(2+6,-1) \\ V1=(8,-1) \\ V2=(2-6,-1) \\ V2=(-4,-1) \end{gathered}`