Question
Asked Dec 24, 2019
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For Exercise, write the standard form of an equation of an ellipse subject to the given conditions. 

Vertices: (6, 0) and (−6, 0);

Foci: (5, 0) and (−5, 0)

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Expert Answer

Step 1

Given:

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Vertices:(6,0) and (-6,0) Foci:(5,0) and (-5,0)

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Step 2

From the given information, the vertices are at distance 6 units from the center. Therefore, the value of a is 6.

Also, the foci are at distance 5 units from the center. Therefore, the value of c is 5.

And the center of the ellipse is the origin.

Now obtain the value of b as shown below.

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a, b and c are related by the formula, b² = a² - c? =(6)' - (5)' = 36 – 25 =11 →b = 11

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Step 3

Here the value of a is greater than b and the vertices are at x axis.

...
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= 1 a? ' b?

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