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Conic sections practice

Graphing ellipses worksheets

Graph standard-form ellipses on equal-scale coordinate grids using exact centers and axial extrema.

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Graph each ellipse on the equal-scale coordinate grid.

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Paper sizes and printing help · More conic sections activities

Graph both semiaxes on one equal-scale grid

Each worksheet contains four standard equations and four coordinate grids from −10 to 10.

Plot the center and four axial extrema, then draw one smooth closed ellipse through those points.

The separate key shows the full ellipse, center and axial points.

Learning objective

What this activity builds

Connect standard ellipse equations with centers, semiaxes and complete coordinate graphs.

Worked example

Graph (x − 2)²/16 + (y + 1)²/4 = 1.

Center (2, −1), horizontal radius 4 and vertical radius 2.

Plot the center and the four axial extrema, then draw the closed ellipse through them.

Teaching notes

Make the practice count

  • Read center signs opposite the signs inside parentheses.
  • Take square roots of both denominators for semiaxis lengths.
  • Plot all four axial extrema before drawing the curve.
  • Use the same horizontal and vertical scale.

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Change the seed for four reproducible equal-scale ellipse graphs.

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Math SheetNameScore/ 4TeacherDateGraphing EllipsesGraph each ellipse on the equal-scale coordinate grid.1.x236+y29=1-10-10-8-8-6-6-4-4-2-2224466881010xy2.x+521+y29=1-10-10-8-8-6-6-4-4-2-2224466881010xy3.x29+y-621=1-10-10-8-8-6-6-4-4-2-2224466881010xy4.x+221+y-3225=1-10-10-8-8-6-6-4-4-2-2224466881010xymath-sheet.comPage 1 / 1

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