Math Problem Statement
Consider the conic section 2x 2 − 2xy + 2y 2 + 4x + 6y + 3 = 0. Rotate and translate the axes to write it in standard form. Hence name the type of conic section.
Solution
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Math Problem Analysis
Mathematical Concepts
Conic Sections
Coordinate Geometry
Rotation of Axes
Translation of Axes
Formulas
Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0
tan(2θ) = B / (A - C)
Rotation transformation: x = x' cos(θ) - y' sin(θ), y = x' sin(θ) + y' cos(θ)
Translation transformation: x'' = x' + h, y'' = y' + k
Theorems
Conic Section Equation Standard Form
Angle of Rotation for Conic Sections
Suitable Grade Level
Undergraduate Level - Calculus and Analytic Geometry
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