Problem preview

G-GPE.3.1 Warmup M3-038-A04-V02

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

Complete squares and extract hyperbola orientation

Problem

Normalize \(9y^2~-~4x^2~=~36\). Give the hyperbola's standard form, center, \(a\), \(b\), opening direction, and vertices.

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The standard form is x²/9 - y²/4 = 1; the center is (0, 0); a = 3 and b = 2; the hyperbola opens horizontal; and its vertices are (-3, 0), (3, 0).

The standard form is y²/4 - x²/9 = 1; the center is (0, 0); a = 2, b = 3; the hyperbola opens vertical; and its vertices are (0, -2), (0, 2).

The standard form is y²/4 - x²/9 = 1; the center is (0, 0); a = 4 and b = 9; the hyperbola opens vertical; and its vertices are (0, -4), (0, 4).

The standard form is y²/(1/9) - x²/(1/4) = 1; the center is (0, 0); a = 1/3 and b = 1/2; the hyperbola opens vertical; and its vertices are (0, -1/3), (0, 1/3).

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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: Complete squares and extract hyperbola orientation