10
QuizMultiple Choice

Conic Sections — Test

Question 10 • Geometry

An ellipse has vertices along the major axis at open paren 0 comma 1 close paren and open paren 0 comma negative 9 close paren The foci of the ellipse are located at open paren 0 comma negative 1 close paren and open paren 0 comma negative 7 close paren The equation of the ellipse is in the form. the fraction with numerator open paren y minus k close paren squared and denominator A squared plus the fraction with numerator open paren x minus h close paren squared and denominator b squared is equal to 1 Which is a correct value for one of the variables shown in the equation?

Answer
A
A is equal to 10
B
k is equal to 0
C
b is equal to 4
D
h is equal to 3

Explanation

The center is the midpoint of the vertices, so it is (0, −4). The distance from the center to either vertex is 5, so the major-axis denominator parameter A is 5. The foci are 3 units from the center, so c = 3; for an ellipse, a² = b² + c², giving b² = 25 − 9 = 16 and b = 4. Therefore, the correct statement is “b is equal to 4.”

AI-written and checked against the verified answer.

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