Question

What are the coordinates of the foci of the conic section shown below?(y + 2)² /16 - (x − 3)² /9 = 1A. (3, -2±5)B.(-2+5,3)C. (-2,3±5)D.(-2+√7,3)

Answer 1

Given the question on the question tab;

Step-by-step explanation:

`((y+2)^2)/(16)-((x-3)^2)/(9)=1`
`h=3,k=-2,a=3,b=4`
`The\text{ }standardform\text{ }is\frac{\text{ }\left(y+2\right)^2}{4^2}-(\left(x - 3\right)^(2))/(3^(2))=1.`
`The\text{ }linear\text{ }eccentricity\text{ }is\text{ }c=\sqrt{b^(2) + a^(2)}=5.`
`\begin{gathered} The\text{ first focus is:} \\ \left(h,k−c\right)=\left(3,−7\right). \\ The\text{ second focus is:} \\ \left(h,k+c\right)=\left(3,3\right) \end{gathered}`

Final answer: