10
QuizMultiple Choice

Equations of Ellipses — Quiz

Question 10 • Geometry

The equation the fraction with numerator x squared and denominator 121 plus the fraction with numerator y squared and denominator 1 is equal to 1 represents an ellipse. Which points are the vertices of the ellipse?

Answer
A
open paren 0 comma negative 11 close paren and open paren 0 comma 11 close paren
B
open paren negative 1 comma 0 close paren and open paren 1 comma 0 close paren
C
open paren 0 comma negative 1 close paren and open paren 0 comma 1 close paren
D
open paren negative 11 comma 0 close paren and open paren 11 comma 0 close paren

Explanation

In the standard ellipse equation, the denominators give the squares of the semiaxis lengths. Since 121 is under x², the horizontal semiaxis has length √121 = 11, so the vertices are (−11, 0) and (11, 0), matching choice A.

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