Answer:
The equation of the ellipse = [tex]\frac{x^2}{1} +\frac{y^2}{37} =1[/tex]
Step-by-step explanation:
Explanation:-
Step(l):-
Given foci of the ellipse is (0,±6)
we know that the foci ( 0, ±C) = (0,±6)
C = 6
The focus is lie on y- axis
Step(ll):-
Given data the vertices are (0,±√37)
The major axes are (0,±a) = (0,±√37)
a = √37
The relation between the focus and semi major axes and semi minor axes are [tex]c^{2} = a^{2} - b^{2}[/tex]
[tex]6^2 = (\sqrt{37} )^{2} - b^{2}[/tex]
[tex]36 = 37 - b^{2}[/tex]
[tex]b^{2} = 37 - 36 =1[/tex]
Step (lll) :-
The equation of the ellipse [tex]\frac{x^2}{b^2} +\frac{y^2}{a^{2} } =1[/tex]
[tex]\frac{x^2}{1^2} +\frac{y^2}{\sqrt({37} )^{2} } =1[/tex]
[tex]\frac{x^2}{1} +\frac{y^2}{37} =1[/tex]
Conclusion:-
The equation of the ellipse = [tex]\frac{x^2}{1} +\frac{y^2}{37} =1[/tex]
