Problem preview

G-GPE.3.1 Warmup M3-038-A01-V03

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

Identify the type of conic by inspecting squared terms and signs in the equation

Problem

What type of conic is represented by \(x^2-y^2=16\)?

Answer choices

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It is a hyperbola because the x² and y² terms have opposite signs, which matches the hyperbola pattern.

It is a parabola because the equation can be rearranged to solve for y, which means it has one curved branch.

It is an ellipse because both x and y are squared, so the graph must be a closed oval shape.

It is a circle because the equation has x² and y² together, which matches the standard circle form.

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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 type of conic by inspecting squared terms and signs in the equation