Given that:
Foci: (0,3), (0,-3)
Co-vertces: (1,0), (-1,0)
The foci are on the y-axis, so the major axis is the y-axis. Thus the equation will have the form:
[tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex]
The foci are (0,3) and (0,-3), so
[tex]c=3\Rightarrow c^2=9[/tex]
The co-vertices are (1, 0) and (-1, 0), so
[tex]b=1\Rightarrow b^2=1[/tex]
The co-vertices and foci are related by the equation
[tex]c^2=a^2-b^2[/tex]
Solving for the square of a.
[tex]\begin{gathered} 9=a^2-1 \\ a^2=10 \end{gathered}[/tex]
Substituate the obtained values into the standard form of he ellipse. Hence the equation of the ellipse is
[tex]\frac{x^2}{1}+\frac{y^2}{10}=1[/tex]
