Understanding Ellipses

What is the definition of an ellipse?

• A set of points with varying distances from a line

• A set of points equidistant from a single point

• A set of points where the sum of distances from two fixed points is constant

• A set of points forming a perfect circle

What is the major axis of an ellipse?

• The shorter axis of the ellipse

• The axis that is perpendicular to the minor axis

• The longer axis of the ellipse

• The axis that passes through the center only

Where do the vertices of an ellipse lie?

• Outside the ellipse

• At the center of the ellipse

• On the major axis

• On the minor axis

What remains constant for any point on an ellipse?

• The distance to the center

• The angle with the major axis

• The sum of distances to the foci

• The distance to the nearest vertex

What is the standard equation of an ellipse with a horizontal major axis?

• x^2 + y^2 = 1

• x^2/b^2 + y^2/a^2 = 1

• x^2 - y^2 = 1

• x^2/a^2 + y^2/b^2 = 1

How do you determine if an ellipse has a horizontal major axis?

• The ellipse is taller than it is wide

• The larger number is under the y^2 term

• The larger number is under the x^2 term

• The ellipse is a perfect circle

What is the formula for finding c^2 in an ellipse?

• c^2 = a^2 * b^2

• c^2 = b^2 - a^2

• c^2 = a^2 - b^2

• c^2 = a^2 + b^2

In the standard form of an ellipse, what does the center (h, k) represent?

• The midpoint of the major axis

• The midpoint of the minor axis

• The center of the ellipse

• The location of one of the foci

How do you find the foci of an ellipse with a vertical major axis?

• Add and subtract c from the x-coordinate of the center

• Add and subtract c from the y-coordinate of the center

• Add and subtract c from both coordinates of the center

• The foci are at the center

What happens to the foci in an ellipse with a horizontal major axis?

• They are on the minor axis

• They are located at the center

• They are outside the ellipse

• They are on the major axis