122503
AssignmentMultiple Select

Equations of Ellipses

Question 122503 • Precalculus

Jeremiah is asked to write the equation of an ellipse. He is given one vertex along the major axis and the location of the center. He realizes he does not have enough information to write the equation. He asks his teacher for one additional piece of information. What information could Jeremiah ask for to help him write the equation? Check all that apply.the location of the focus nearest the given vertexthe location of the focus nearest the other vertexthe location of the other vertex along the major axisthe location of one covertex along the minor axisthe location of the directrix nearest the given vertexthe location of the directrix nearest the other vertexthe length of the minor axis

Answer
A
the location of the focus nearest the given vertex
B
the location of the focus nearest the other vertex
C
the location of the other vertex along the major axis
D
the location of one covertex along the minor axis
E
the location of the directrix nearest the given vertex
F
the location of the directrix nearest the other vertex
G
the length of the minor axis

Explanation

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.

AI-written and checked against the verified answer.

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