4. A horizontal ellipse, centered at the origin has a major axis of 10 units and minor axis of 8 units. Write the
equation of the ellipse.

Step-by-step explanation:

For ellipses, the length of the major axis is represents as:

Major axis =

where is called the semi-major axis.

In this case since the major axis is equal to 10 units:

solving for the semi-major axis :

and also the minor axis of an ellipse is represented as:

Minor axis =

where  is called the semi-minor axis.

Since the minor axis has a length of 8 units:

solving for b:

Now we can use the equation for an ellipse centered at the origin (0,0):

and substituting the values for and :

and finall we simplify the expression to get the equation of the ellipse:

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