MATH SOLVE

3 months ago

Q:
# Which of the following statements about an ellipse is NOT true?(a) An ellipse with a large eccentricity looks much more elongated (stretched out) than an ellipse with a small eccentricity.(b) The focus of an ellipse is always located precisely at the center of the ellipse.(c) A circle is considered to be a special type of ellipse.(d) The semimajor axis of an ellipse is half the length of the longest line that you can draw across an ellipse.

Accepted Solution

A:

Answer: (b) The focus of an ellipse is always located precisely at the center of the ellipse.Step-by-step explanation:An ellipse is defined as "a closed curve with two axes of symmetry (major axis and minor axis) that results in cutting the surface of a cone by an oblique plane to the axis of symmetry with an angle greater than that of the generatrix with respect to the axis of revolution". That is why the ellipse is considered a conic figure.
To understand it better: an ellipse has two points on its major axis that are equidistant from the center , which are called foci, being this distance constant. In addition, the eccentricity allows to know how far the foci are from the center of the ellipse.
Therefore, the statement that indicates an ellipse has only one focus located precisely at the center is incorrect.