Math Problem Statement

Transform the equation 3x^2 + 8xy + 3y^2 - 2x + 2y - 2 = a^2 referred to new axes through (-1, 1) rotated through an angle π/4. Solve similar transformation-related problems in the list.

Solution

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Math Problem Analysis

Mathematical Concepts

Conic Sections
Coordinate Geometry
Transformation of Axes
Rotation of Axes
Shifting of Origin

Formulas

Rotation of axes: x = x'cosθ - y'sinθ, y = x'sinθ + y'cosθ
Shifting of origin: x' = x - h, y' = y - k

Theorems

Equation transformation through rotation
Shifting of origin for conics
Properties of conic sections under transformations

Suitable Grade Level

Grades 11-12 or early college mathematics

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