The General Equation of Conic Sections — Quiz

Question 7 • Precalculus

Graph the fraction with numerator open paren x minus 4 close paren squared and denominator 4 plus the fraction with numerator y squared and denominator 9 is equal to 1

Answer

Image with description On a coordinate plane, an Ellipse has center point (negative 4, 0) and goes through (negative 1, 0), (negative 4, 2), (negative 7, 0) and (negative 4, negative 2).

Image with description On a coordinate plane, an Ellipse has center (negative 4, 0) and goes through (negative 2, 0), (negative 4, 3), (negative 6, 0) and (negative 4, negative 3).

Image with description On a coordinate plane, an Ellipse has center point (4, 0) and goes through (4, 2), (7, 0), (4, negative 2), and (1, 0).

Image with description On a coordinate plane, an Ellipse has center (4, 0) and goes through (6, 0), (4, negative 3), (2, 0) and (4, 3).

Explanation

The equation is in ellipse form: (x − 4)²/4 + y²/9 = 1. Its center is (4, 0), with a horizontal radius of 2 and a vertical radius of 3, so its endpoints are (2, 0), (6, 0), (4, 3), and (4, −3). Choice B shows this ellipse.

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