Question

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which of these is the best definition of an ellipse?

a. the set of all points in a plane that are a certain distance from a single point
b. the set of all points in a plane that are equidistant from a single point and a line
c. the set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant
d. the set of all points in a plane for which the difference between the distances to two fixed points equals a certain constant

Explanation:

Analyze the geometric definitions of conic sections

• Option A defines a circle (points at a constant distance from a single point).
• Option B defines a parabola (points equidistant from a single point, the focus, and a line, the directrix).
• Option C defines an ellipse (points where the sum of the distances to two fixed points, the foci, is constant).
• Option D defines a hyperbola (points where the absolute difference of the distances to two fixed points is constant).

Identify the correct definition for an ellipse

• The definition of an ellipse is the locus of points where the sum of the distances to two fixed points is a constant.
• This matches Option C.

Answer:

• A. The set of all points in a plane that are a certain distance from a single point
• B. The set of all points in a plane that are equidistant from a single point and a line
• C. The set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant (Correct answer)
• D. The set of all points in a plane for which the difference between the distances to two fixed points equals a certain constant