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Alika [10]
2 years ago
7

Find the equation of an ellipse satisfying the given conditions.

Mathematics
1 answer:
Lana71 [14]2 years ago
8 0

The equation of the ellipse is \frac{x^2}{49}  + \frac{y^2}{65}  = 1

<h3>How to determine the ellipse equation?</h3>

The given parameters are:

  • Foci: (-4, 0) and (4, 0)
  • Length of major axis = 14

The above means that:

c = 4 and

The semi-major axis, a = 7 i.e 14/2

Calculate b using

b = \sqrt{c^2 + a^2

So, we have:

b = \sqrt{4^2 + 7^2

b = \sqrt{65

Square both sides

b^2 = 65

The standard form of the ellipse is represented as:

\frac{x^2}{a^2}  + \frac{y^2}{b^2}  = 1

This gives

\frac{x^2}{7^2}  + \frac{y^2}{65}  = 1

Evaluate

\frac{x^2}{49}  + \frac{y^2}{65}  = 1

Hence, the equation of the ellipse is \frac{x^2}{49}  + \frac{y^2}{65}  = 1

Read more about ellipse at:

brainly.com/question/14281133

#SPJ1

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