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Conic sections practice

Writing equations of hyperbolas worksheets

Construct exact standard-form hyperbola equations from general equations, vertices, foci, conjugate-axis data and asymptotes.

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Use the given information to write each hyperbola in standard form.

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Build standard form from nine kinds of givens

Each worksheet contains eight constructions selected from general equations, axial point pairs, exact lengths and asymptote equations.

Find the common center, transverse direction and exact squared radii, then place the positive transverse term first.

The separate key derives one exact equation from the printed givens.

Learning objective

What this activity builds

Use exact geometric or algebraic givens to determine one axis-aligned hyperbola in standard form.

Worked example

Write the hyperbola with vertices (−3, 0), (3, 0) and foci (−5, 0), (5, 0).

x²/9 − y²/16 = 1.

Here a² = 9 and c² = 25, so b² = c² − a² = 16.

Teaching notes

Make the practice count

  • Find the common center before measuring axial distances.
  • Put the positive term first in the transverse direction.
  • Verify that both asymptotes intersect at the center.
  • Use full conjugate-axis length as 2b.

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Choose one or more given forms, then change the seed for eight reproducible hyperbola equations.

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Math SheetNameScore/ 8TeacherDateWriting Equations of HyperbolasUse the given information to write each hyperbola in standard form.1.Vertices:(5,-6),(-13,-6)Center-to-focus distance:9·22.Vertices:(-8,2),(-8,0)Conjugate-axis length:23.Vertices:(-1,7),(-3,7)Conjugate endpoints:(-2,15),(-2,-1)4.Foci:(3,8+61),(3,8-1·61)Asymptotes:y=65·x+225,y=-65·x+5855.Foci:(2,-3+2·17),(2,-3-2·17)Conjugate-axis length:46.4·x2-1·y2-48·x+16·y+76=07.Vertices:(17,8),(-7,8)Asymptotes:y=34·x+174,y=-34·x+4748.Vertices:(0,11),(0,3)Foci:(0,7+65),(0,7-1·65)math-sheet.comPage 1 / 1

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