Conic sections
Properties of hyperbolas worksheets
Find exact vertices, foci and opening directions from horizontal and vertical standard-form hyperbola equations.
Preview and downloadConic sections practice
Graphing hyperbolas worksheets
Graph both visible branches, vertices, construction rectangles and asymptotes on equal-scale coordinate grids.
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Graph each hyperbola on the equal-scale coordinate grid.
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Graph two branches and their asymptotes
Each worksheet contains four standard equations and four equal-scale coordinate grids from −10 to 10.
Draw the construction rectangle and its diagonal asymptotes, then plot the two separate branches through the vertices.
The separate key shows both clipped branches, both asymptotes, the rectangle and exact vertices.
Learning objective
What this activity builds
Connect standard hyperbola form with its center, vertices, asymptotes and two open branches.
Worked example
Graph x²/9 − y²/16 = 1.
Center (0, 0), vertices (−3, 0) and (3, 0), asymptotes y = ±(4/3)x.
Use a = 3 and b = 4 to draw the construction rectangle, its diagonals and the two branches opening left and right.
Teaching notes
Make the practice count
- The positive term identifies the opening direction.
- Take square roots of both denominators for the construction rectangle.
- Draw asymptotes through opposite rectangle corners.
- Keep the two branches separate and approach the asymptotes.
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Customize the practice
Choose your options, update the preview, then download the exact same pages.
Change the seed for four reproducible equal-scale hyperbola graphs.
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