Respuesta :
Answer:
[tex]\frac{x^2}{25} +\frac{y^2}{16} =1[/tex]
Step-by-step explanation:
For ellipses, the length of the major axis is represents as:
Major axis = [tex]2a[/tex]
where [tex]a[/tex] is called the semi-major axis.
In this case since the major axis is equal to 10 units:
[tex]10=2a[/tex]
solving for the semi-major axis [tex]a[/tex] :
[tex]a=10/2\\a=5[/tex]
and also the minor axis of an ellipse is represented as:
Minor axis = [tex]2b[/tex]
where [tex]b[/tex] is called the semi-minor axis.
Since the minor axis has a length of 8 units:
[tex]8=2b[/tex]
solving for b:
[tex]b=8/2\\b=4[/tex]
Now we can use the equation for an ellipse centered at the origin (0,0):
[tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]
and substituting the values for [tex]a[/tex] and [tex]b[/tex]:
[tex]\frac{x^2}{5^2} +\frac{y^2}{4^2} =1[/tex]
and finall we simplify the expression to get the equation of the ellipse:
[tex]\frac{x^2}{25} +\frac{y^2}{16} =1[/tex]
