Answer:
The equation of ellipse is [tex]\frac{x^2}{25}+\frac{y^2}{9}=1[/tex].
Step-by-step explanation:
The center of ellipse is origin because the ellipse has foci at (4, 0) and (-4, 0); y-intercepts (0, 3) and (0, -3).
The general equation of an ellipse is
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
Where, a is major axis and b is minor.
The y-intercepts are (0, 3) and (0, -3). So, the value of b is 3.
The foci of ellipse is [tex](\pm c,0)[/tex].The relation between foci and major, minor axis is
[tex]c^2=a^2-b^2[/tex]
[tex](4)^2=a^2-(3)^2[/tex]
[tex]16=a^2-9[/tex]
[tex]a^2=25[/tex]
[tex]a=5[/tex]
The equation of ellipse is
[tex]\frac{x^2}{5^2}+\frac{y^2}{3^2}=1[/tex]
[tex]\frac{x^2}{25}+\frac{y^2}{9}=1[/tex]
