If the eccentricity of an ellipse is 0.43 and the length of its major axis is 11 units, how far from the center are the foci located?

2.365 unit far away the center are the foci located.      

Step-by-step explanation:

Given : If the eccentricity of an ellipse is 0.43 and the length of its major axis is 11 units.

To find : How far from the center are the foci located?

Solution :

The eccentricity of an ellipse is defined as

Where, e is the eccentricity

c is the distance from center to focus

a is the distance between focus to vertex.

We have given,

Eccentricity of an ellipse is 0.43 i.e. e=0.43

The distance between focus to vertex is the half of the length of its major axis.

i.e.

Substitute in the formula,

Therefore, 2.365 unit far away the center are the foci located.                      

So first you need to open the brackets, so it would be x+2+4x-122=180. Then we can add the 4x and the other x to make 5x, and then by doing 2-122 we get -120. This gives us the equation 5x-120=180. We then isolate the variable by moving the -120 to the other side of the equation and becoming a positive, so it would look like 5x=180+120. Then, we have 5x=300. 300 divides by 5 is 60 making X=60. Hope this helps!