Answer:
[tex]\frac{(x)^{2}}{49}+\frac{(y)^{2}}{1}=1[/tex]
Step-by-step explanation:
In this problem we have a horizontal ellipse, because the major axis is the x-axis
The equation of a horizontal ellipse is equal to
[tex]\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}} =1[/tex]
where
(h,k) is the center of the ellipse
a and b are the respective vertices distances from center
we have
vertices at (7, 0) and (-7, 0)
co-vertices at (0, 1) and (0, -1)
so
The center is the origin (0.0) (The center is the midpoint of the vertices)
a=7
b=1
substitute
[tex]\frac{(x-0)^{2}}{7^{2}}+\frac{(y-0)^{2}}{1^{2}}=1[/tex]
[tex]\frac{(x)^{2}}{49}+\frac{(y)^{2}}{1}=1[/tex]
