The distance from the origin to one of the ellipse's focus is

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Multiple Choice

The distance from the origin to one of the ellipse's focus is

Explanation:
In an ellipse, the distance from the center to a focus along the major axis is c, with c^2 = a^2 − b^2. The eccentricity e is defined as e = c / a, so c = a · e. Therefore, the distance from the origin to a focus equals the semi-major axis a times the first eccentricity e. This matches the option that multiplies the first eccentricity by a. The other forms mix in the linear eccentricity or the semi-minor axis in ways that do not give the actual focal distance.

In an ellipse, the distance from the center to a focus along the major axis is c, with c^2 = a^2 − b^2. The eccentricity e is defined as e = c / a, so c = a · e. Therefore, the distance from the origin to a focus equals the semi-major axis a times the first eccentricity e. This matches the option that multiplies the first eccentricity by a. The other forms mix in the linear eccentricity or the semi-minor axis in ways that do not give the actual focal distance.

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