Question

use a following question to answer the questions below (the equation in the picture)is the lips horizontal or vertical besides graphing how do you knowfind the fociwhats the eccentricity? round to two decimals

Answer 1

Given data:

The given equation of ellipe is

`\begin{gathered} ((x+2)^2)/(36)+((y-3)^2)/(9)=1 \\ ((x+2)^2)/(6^2)+((y-3)^2)/(3^2)=1 \end{gathered}`

The eccentricity of the ellipse is,

`\begin{gathered} e=\sqrt[]{1-(b^2)/(a^2)} \\ =\sqrt[]{1-(9)/(36)} \\ =\sqrt[]{(25)/(36)} \\ =(5)/(6) \end{gathered}`

The focii is,

`\begin{gathered} (3,6e)\text{ , (3,-6e)} \\ (3,5),\text{ (3,-5)} \end{gathered}`

Thus, the focii is (3,5), (3,-5) and eccentricity is 5/6 and lips are horizontal as major axis is greater than minor axis.