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Worksheet: Conic Sections in Standard Form

Q1:

Consider the conic given by the equation 4 π‘₯ + 3 𝑦 βˆ’ 3 2 π‘₯ + 6 𝑦 + 5 5 = 0   .

Write the equation in standard form.

  • A ( π‘₯ βˆ’ 4 ) + ( 𝑦 + 1 ) = 1 2  
  • B ( π‘₯ βˆ’ 4 ) 3 βˆ’ ( 𝑦 + 1 ) 4 = 1  
  • C ( π‘₯ + 4 ) 3 + ( 𝑦 βˆ’ 1 ) 4 = 1  
  • D ( π‘₯ βˆ’ 4 ) 3 + ( 𝑦 + 1 ) 4 = 1  
  • E ( π‘₯ + 4 ) 3 βˆ’ ( 𝑦 βˆ’ 1 ) 4 = 1  

Hence, describe the conic.

  • AAn ellipse with center ( 4 , βˆ’ 1 )
  • BAn ellipse with center ( βˆ’ 4 , 1 )
  • CA hyperbola with center ( 4 , βˆ’ 1 )
  • DA circle with center ( 4 , βˆ’ 1 )
  • EA hyperbola with center ( βˆ’ 4 , 1 )

Q2:

Which type of conic is described by the equation 5 π‘₯ βˆ’ 9 𝑦 βˆ’ 1 0 π‘₯ + 9 0 𝑦 βˆ’ 2 6 5 = 0 2 2 ?

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