Problem preview

G-GPE.3.1 Warmup M3-038-A12-V02

Complete the square for general quadratic conic equations; identify and graph circles, ellipses, parabolas, or hyperbolas.

Identify the graph features of a conic from its standard-form equation

Problem

Identify the conic represented by \((x~+~2)^2/9~+~(y~-~4)^2/25~=~1\). Give its center and use the denominator placement to determine the major-axis orientation.

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This equation is an ellipse in standard form, so the center is (2, 4) and the larger denominator is under the y-term, which means the major axis is vertical.

This equation is an ellipse in standard form, so the center is (-2, 4) and because the x-term comes first, the major axis is horizontal.

This equation is an ellipse in standard form, so the center is (-2, 4) and the larger denominator is under the y-term, which means the major axis is vertical.

This equation is a circle in standard form, so the center is (-2, 4) and the graph has the same radius in every direction.

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Curriculum context

Course: Math III
Standard: G-GPE.3.1
Category: Geometry
Domain: Expressing Geometric Properties with Equations
Objective: Complete the square for general quadratic conic equations; identify and graph circles, ellipses, parabolas, or hyperbolas.
Problem type: Identify the graph features of a conic from its standard-form equation