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Analytic Geometry2D

Translation and Rotation of Axes - Theory & Concepts - Analytic Geometry Curve Transformation

Transformation of coordinates through translation and rotation of the axes, and eliminating the xy-term in conic sections.

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2.0
-1.0

Standard Ellipse (h=0, k=0):

x²/9 + y²/4 = 1

Translating axes shifts standard coordinates to: (x - h) and (y - k).

Shifted ellipse centered at (2, -1)Grid lineGrid backgroundOriginal Horizontal AxisOriginal Vertical AxisTranslated Horizontal AxisTranslated Vertical AxisShifted Ellipse CurveCenter Point at (2, -1)
(x−2.0)29+(y−(−1.0))24=1\frac{(x - 2.0)^2}{9} + \frac{(y - (-1.0))^2}{4} = 1

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