Math Problem Statement

Identify a and b for the hyperbola with equation x2a2-y2b2=1.

a = b =

Solution

The given equation of the hyperbola is:

x2a2y2b2=1\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1

This is the standard form of a hyperbola with the transverse axis along the xx-axis. To identify aa and bb, follow these steps:

  1. Understand the parameters:

    • a2a^2 is the denominator under x2x^2.
    • b2b^2 is the denominator under y2y^2.
  2. Extract aa and bb:

    • aa is the square root of the denominator under x2x^2.
    • bb is the square root of the denominator under y2y^2.

Final Values:

  • a=a2a = \sqrt{a^2}
  • b=b2b = \sqrt{b^2}

Please provide the specific denominators (values of a2a^2 and b2b^2) from the hyperbola equation so I can calculate the exact aa and bb values for you.

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Math Problem Analysis

Mathematical Concepts

Analytic Geometry
Hyperbolas
Conic Sections

Formulas

Standard form of a hyperbola: (x^2/a^2) - (y^2/b^2) = 1
Relationship: a = sqrt(a^2), b = sqrt(b^2)

Theorems

Definition of a hyperbola
Properties of conic sections

Suitable Grade Level

Grades 10-12