Answer:
[tex]=\frac{x^2}{16} +\frac{y^2}{49}=1[/tex]
Step-by-step explanation:
The equation of this ellipse is
[tex]\frac{(x-h)^2}{b^2} +\frac{y-k)^2}{a^2} =1[/tex]
for a vertical oriented ellipse where;
(h,k) is the center
c=distance from center to the foci
a=distance from center to the vertices
b=distance from center to the co-vertices
You know center of an ellipse is half way between the vertices , hence the center (h,k) of this ellipse is (0,0) and its is vertical oriented ellipse
Given that
a= distance between the center and the vertices, a=7
c=distance between the center and the foci, c=√33
Then find b
[tex]a^2-b^2=c^2\\\\b^2=a^2-c^2\\\\\\b^2=7^2-(\sqrt{33} )^2\\\\\\b^2=49-33=16\\\\\\b^2=16[/tex]
The equation for the ellipse will be
[tex]\frac{(x-0)^2}{16} +\frac{(y-0)^2}{49} =1\\\\\\=\frac{x^2}{16} +\frac{y^2}{49} =1[/tex]
