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Worksheet: Discriminant of a Conic Section

Q1:

By calculating the discriminant, identify the type of conic that is described by the equation π‘₯ + 𝑦 + 1 0 π‘₯ βˆ’ 4 𝑦 + 2 8 = 0 2 2 .

  • AA parabola
  • BA hyperbola
  • CAn ellipse
  • DA circle

Q2:

The general equation of a conic has the form 𝐴 π‘₯ + 𝐡 π‘₯ 𝑦 + 𝐢 𝑦 + 𝐷 π‘₯ + 𝐸 𝑦 + 𝐹 = 0 2 2 .

Consider the equation 2 π‘₯ βˆ’ 3 𝑦 βˆ’ 1 6 π‘₯ βˆ’ 3 0 𝑦 βˆ’ 4 9 = 0 2 2 .

Calculate the value of the discriminant 𝐡 βˆ’ 4 𝐴 𝐢 2 .

Hence, identify the conic described by the equation.

  • ACircle
  • BEllipse
  • CParabola
  • DHyperbola

Q3:

The general equation of a conic has the form 𝐴 π‘₯ + 𝐡 π‘₯ 𝑦 + 𝐢 𝑦 + 𝐷 π‘₯ + 𝐸 𝑦 + 𝐹 = 0 2 2 .

Which of the following conditions would allow us to conclude that it is an ellipse?

  • A 𝐡 βˆ’ 4 𝐴 𝐢 > 0 2
  • B 𝐡 βˆ’ 4 𝐴 𝐢 = 0 2
  • C 𝐡 βˆ’ 4 𝐴 𝐢 < 0 2 , 𝐡 = 0 , and 𝐴 = 𝐢
  • D 𝐡 βˆ’ 4 𝐴 𝐢 < 0 2 and either 𝐡 β‰  0 or 𝐴 β‰  𝐢