An ellipse has foci (0,+-3) and vertices (0,+-4). What is the eccentricity of the ellipse?
Please help.
To find the eccentricity of an ellipse, you can use the formula:
eccentricity (e) = √(1 - (b^2 / a^2))
Where "a" represents the distance from the center to a vertex, and "b" represents the distance from the center to a focus.
In this case, the distance from the center to a vertex is given as 4, and the distance from the center to a focus is given as 3.
So, plugging these values into the eccentricity formula, we get:
eccentricity (e) = √(1 - (3^2 / 4^2))
Calculating the values inside the square root:
eccentricity (e) = √(1 - (9 / 16))
Simplifying:
eccentricity (e) = √(7 / 16)
Taking the square root:
eccentricity (e) ≈ √0.4375
e ≈ 0.66
Therefore, the eccentricity of the ellipse is approximately 0.66.