Question

if the vertices and foci of the equation below is in th form (-a,0) and (a,0) and (-c,0) and (c,0), respectively, find a+c.

Answer 1

this is an equation of ellipse

where

`a=3,b=2`

for ellipse

`c^2=a^2-b^2`

so

`\begin{gathered} c^2=9-4 \\ c^2=5 \\ c=\pm\sqrt[]{5} \end{gathered}`

hence

`a+c=3\pm\sqrt[]{5}`