Question

Find the equation of an ellipse satisfying the given conditions.

Answer 1

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

How to determine the ellipse equation?

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