Lesson Worksheet: Equation of a Hyperbola Mathematics

In this worksheet, we will practice writing the equation of a hyperbola and finding a hyperbola’s vertices and foci using its equation and graph.

Q1:

Write the equation of the rectangular hyperbola passing through (1,1) with asymptotes meeting at (3,4).

  • A𝑦=10𝑥34
  • B𝑦=20𝑥+34
  • C𝑦=10𝑥+4+3
  • D𝑦=1𝑥59
  • E𝑦=24𝑥47

Q2:

The graph shows a sketch of the hyperbola given by the equation 4𝑦𝑥+8𝑦10𝑥=25.

Give the coordinates of the center 𝐶.

  • A𝐶(5,1)
  • B𝐶(1,5)
  • C𝐶(1,5)
  • D𝐶(5,1)

Give the coordinates of the vertices 𝑉 and 𝑉.

  • A𝑉(3,1), 𝑉(7,1)
  • B𝑉(5,0), 𝑉(5,2)
  • C𝑉(4,1), 𝑉(6,1)
  • D𝑉(5,1), 𝑉(5,3)

Give the coordinates of the foci 𝐹 and 𝐹.

  • A𝐹5+5,1, 𝐹55,1
  • B𝐹5,1+5, 𝐹5,15
  • C𝐹5,1+5, 𝐹5,15
  • D𝐹5+5,1, 𝐹55,1

Give the equations of the asymptotes 𝐴 and 𝐴.

  • A𝐴𝑦+1=12(𝑥+5):, 𝐴𝑦+1=12(𝑥+5):
  • B𝐴𝑦+1=2(𝑥+5):, 𝐴𝑦+1=2(𝑥+5):
  • C𝐴𝑦+1=12(𝑥5):, 𝐴𝑦+1=12(𝑥5):
  • D𝐴𝑦1=12(𝑥+5):, 𝐴𝑦1=12(𝑥+5):

Q3:

The graph shows a sketch of the hyperbola given by the equation (𝑦2)25(𝑥+3)2=1.

Give the coordinates of the center 𝐶.

  • A𝐶(2,3)
  • B𝐶(3,2)
  • C𝐶(2,3)
  • D𝐶(3,2)

Give the coordinates of the vertices 𝑉 and 𝑉.

  • A𝑉(2,2), 𝑉(8,2)
  • B𝑉3,2+2, 𝑉3,22
  • C𝑉3+2,2, 𝑉32,2
  • D𝑉(3,7), 𝑉(3,3)

Give the coordinates of the foci 𝐹 and 𝐹.

  • A𝐹3,2+33, 𝐹3,233
  • B𝐹3+33,2, 𝐹333,2
  • C𝐹3,2+33, 𝐹3,233
  • D𝐹3+33,2, 𝐹333,2

Give the equations of the asymptotes 𝐴 and 𝐴.

  • A𝐴𝑦2=52(𝑥3):, 𝐴𝑦2=52(𝑥3):
  • B𝐴𝑦2=52(𝑥+3):, 𝐴𝑦2=52(𝑥+3):
  • C𝐴𝑦+2=52(𝑥+3):, 𝐴𝑦+2=52(𝑥+3):
  • D𝐴𝑦2=25(𝑥+3):, 𝐴𝑦2=25(𝑥+3):

Q4:

The graph shows a sketch of the hyperbola given by the equation (𝑥3)4(𝑦1)16=1.

Give the coordinates of the center 𝐶.

  • A𝐶(3,1)
  • B𝐶(1,3)
  • C𝐶(1,3)
  • D𝐶(3,1)

Give the coordinates of the vertices 𝑉 and 𝑉.

  • A𝑉(5,3), 𝑉(3,3)
  • B𝑉(5,1), 𝑉(1,1)
  • C𝑉(3,3), 𝑉(1,3)
  • D𝑉(7,1), 𝑉(1,1)

Give the coordinates of the foci 𝐹 and 𝐹.

  • A𝐹1+25,3, 𝐹125,3
  • B𝐹3+25,1, 𝐹325,1
  • C𝐹3+25,1, 𝐹325,1
  • D𝐹1+25,3, 𝐹125,3

Give the equations of the asymptotes 𝐴 and 𝐴.

  • A𝐴𝑦1=2(𝑥+3):, 𝐴𝑦1=2(𝑥+3):
  • B𝐴𝑦1=2(𝑥3):, 𝐴𝑦1=2(𝑥3):
  • C𝐴𝑦1=12(𝑥3):, 𝐴𝑦1=12(𝑥3):
  • D𝐴𝑦+1=2(𝑥3):, 𝐴𝑦+1=2(𝑥3):

Q5:

The graph shows a sketch of the hyperbola given by the equation 4𝑥9𝑦16𝑥182𝑦=29.

Give the coordinates of the center 𝐶.

  • A𝐶(2,1)
  • B𝐶(1,2)
  • C𝐶(2,1)
  • D𝐶(1,2)

Give the coordinates of the vertices 𝑉 and 𝑉.

  • A𝑉(5,1),𝑉(1,1)
  • B𝑉(4,1),𝑉(0,1)
  • C𝑉(2,2),𝑉(4,2)
  • D𝑉(1,2),𝑉(3,2)

Give the coordinates of the foci 𝐹 and 𝐹.

  • A𝐹2+13,1,𝐹213,1
  • B𝐹2,1+13,𝐹2,113
  • C𝐹2+13,1,𝐹213,1
  • D𝐹2,1+13,𝐹2,113

Give the equations of the asymptotes 𝐴 and 𝐴.

  • A𝐴𝑦+1=32(𝑥2),𝐴𝑦+1=32(𝑥2)
  • B𝐴𝑦1=23(𝑥2),𝐴𝑦1=23(𝑥2)
  • C𝐴𝑦+1=23(𝑥2),𝐴𝑦+1=23(𝑥2)
  • D𝐴𝑦+1=23(𝑥+2),𝐴𝑦+1=23(𝑥+2)

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