Worksheet: Conic Sections in Standard Form

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 4 𝑥 + 3 𝑦 3 2 𝑥 + 6 𝑦 + 5 5 = 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 )
  • BAn ellipse with center ( 4 , 1 )
  • CA hyperbola with center ( 4 , 1 )
  • DA circle with center ( 4 , 1 )
  • EA hyperbola with center ( 4 , 1 )

Q2:

Which type of conic is described by the equation 5 𝑥 9 𝑦 1 0 𝑥 + 9 0 𝑦 2 6 5 = 0 2 2 ?

  • AAn ellipse
  • BA circle
  • CA parabola
  • DA hyperbola

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