Ok, so
We want to find the equation of an ellipse centered at the origin with a horizontal major axis of 8 units and a minor axis of 6 units.
For this, let's remember the form of the equation of an ellipse:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
Where the center of the ellipse is located at the point (h,k).
If the ellipse is centered at the origin, then, h=0 and k=0, so the form of our equation will be:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
Now, we're given that our ellipse has a horizontal major axis of 8 units and a minor axis of 6 units. Since the major and minor axis are given by the parameters 2a and 2b, then, a=4 and b=3. the greater number will divide the x² term and a>b.
So, the equation of this ellipse is:
[tex]\frac{x^2}{16}+\frac{y^2}{9}=1[/tex]
The graph of this ellipse will be something like:
