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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.

User Torleif
by
8.4k points

1 Answer

3 votes

Answer:


(x^2)/(25) +(y^2)/(16) =1

Explanation:

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

Major axis =
2a

where
a is called the semi-major axis.

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


10=2a

solving for the semi-major axis
a :


a=10/2\\a=5

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

Minor axis =
2b

where
b is called the semi-minor axis.

Since the minor axis has a length of 8 units:


8=2b

solving for b:


b=8/2\\b=4

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


(x^2)/(a^2) +(y^2)/(b^2) =1

and substituting the values for
a and
b:


(x^2)/(5^2) +(y^2)/(4^2) =1

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


(x^2)/(25) +(y^2)/(16) =1

User Adewale
by
7.7k points

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