Question 122503 • Precalculus
The given center and major-axis vertex establish the major-axis direction and the semi-major length a. To write the ellipse equation, Jeremiah also needs the semi-minor length b. Either focus gives the distance c from the center, so he can use b² = a² − c²; a covertex or the minor-axis length gives b directly. A directrix gives the eccentricity e, which determines b using b² = a²(1 − e²). The other major-axis vertex only confirms the already-known major-axis length, so it does not provide the missing information.
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