Worksheet: Identifying Conic Sections

In this worksheet, we will practice converting the general form of conic section equations into any of the standard forms.

Q1:

Consider the conic given by the equation 4𝑥+3𝑦32𝑥+6𝑦+55=0.

Write the equation in standard form.

  • A ( 𝑥 4 ) + ( 𝑦 + 1 ) = 1 2
  • B ( 𝑥 4 ) 3 + ( 𝑦 + 1 ) 4 = 1
  • C ( 𝑥 + 4 ) 3 ( 𝑦 1 ) 4 = 1
  • D ( 𝑥 + 4 ) 3 + ( 𝑦 1 ) 4 = 1
  • E ( 𝑥 4 ) 3 ( 𝑦 + 1 ) 4 = 1

Hence, describe the conic.

  • AAn ellipse with center (4,1)
  • BA circle with center (4,1)
  • CA hyperbola with center (4,1)
  • DA hyperbola with center (4,1)
  • EAn ellipse with center (4,1)

Q2:

Which type of conic is described by the equation 5𝑥9𝑦10𝑥+90𝑦265=0?

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

Q3:

By calculating the discriminant, identify the type of conic that is described by the equation 𝑥+𝑦+10𝑥4𝑦+28=0.

  • AA parabola
  • BAn ellipse
  • CA circle
  • DA hyperbola

Q4:

The general equation of a conic has the form 𝐴𝑥+𝐵𝑥𝑦+𝐶𝑦+𝐷𝑥+𝐸𝑦+𝐹=0.

Consider the equation 2𝑥3𝑦16𝑥30𝑦49=0.

Calculate the value of the discriminant 𝐵4𝐴𝐶.

Hence, identify the conic described by the equation.

  • AParabola
  • BHyperbola
  • CEllipse
  • DCircle

Q5:

The general equation of a conic has the form 𝐴𝑥+𝐵𝑥𝑦+𝐶𝑦+𝐷𝑥+𝐸𝑦+𝐹=0.

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

  • A 𝐵 4 𝐴 𝐶 < 0 and either 𝐵0 or 𝐴𝐶
  • B 𝐵 4 𝐴 𝐶 < 0 , 𝐵 = 0 , and 𝐴=𝐶
  • C 𝐵 4 𝐴 𝐶 > 0
  • D 𝐵 4 𝐴 𝐶 = 0

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