Answer:
(0, - √65) and (0, √65)
Step-by-step explanation:
Standard Form Equation of an Ellipse
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
a - semi-major axis
b - semi-minor axis
The formula of a foci:
[tex]F=\sqrt{a^2-b^2}\ if\ a>b\ \text{horizontal elipse}\\\\F=\sqrt{b^2-a^2}\ if\ a<b\ \text{vertical elipse}[/tex]
We have:
[tex]\dfrac{x^2}{16}+\dfrac{y^2}{81}=1\\\\\dfrac{x^2}{4^2}+\dfrac{y^2}{9^2}=1[/tex]
a = 4, b = 9 → a < b → vertical
The foci:
[tex]F=\sqrt{9^2-4^2}=\sqrt{81-16}=\sqrt{65}[/tex]
The coordinates of foci:
[tex](-F,\ 0)\ and\ (F,\ 0)\ if\ a>b\\\\(0,\ -F)\ and\ (0,\ F)\ if\ a<b[/tex]
Substitute:
[tex](0,\ -\sqrt{65})\ and\ (0,\ \sqrt{65})[/tex]
