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Conic Sections
Quiz: Hyperbola Module

Name:___________________________________
Instructions:Answer all the following questions in the space provided. Simplify all answers.
  1. Identify the centre, opening direction, vertices and the slopes of the asymptotes for the hyperbola defined by:

    a) x2/ 49 - y2/ 16 = 1

    b) -x2/ 4 + (y + 4)2/ 64 = 1

    c) (x + 8)2/ 9 - (y - 16)2/ 8 = 1

    d) -(x + 6)2/ 25 + (y - 12)2/ 7 = 1


    a
    b
    c
    d
    Centre  
          		 
          		 
          		 
     
    Opening Direction  
          		 
          		 
          		 
     
    Vertices  
          		 
          		 
          		 
     
    Slopes of Asymptotes  
          		 
          		 
          		 
     



  2. A hyperbola centred at the origin opens up and down and has asymptotes with slopes of +3/2 and -3/2.

    a) Write the equation of this hyperbola in standard form. _____________________________

    b) Write the equation of this hyperbola in general form.
    ______________________________
    c) Sketch the graph of this hyperbola on the provided graph paper.

  3. A hyperbola centred at (3, 1) opens left and right and has asymptotes with slopes of +5 and -5.

    a) Write the equation of this hyperbola in standard form. _____________________________

    b) Write the equation of this hyperbola in general form.
    ______________________________
    c) Sketch the graph of this hyperbola on the provided graph paper.

  4. Describe the effect that varying h and k in the standard equations (x - h)2/ a2 - (y - k)2/ b2 = 1 and -(x - h)2/ a2 + (y - k)2/ b2 = 1 has on the graph of a hyperbola by completing the following chart.

    The Effect of h and k on the graphs of (x - h)2/ a2 - (y - k)2/ b2 = 1 and -(x - h)2/ a2 + (y - k)2/ b2 = 1
    Variable The value of the variable decreases The value of the variable increases The value of the variable is 0.
    h
    		 
     
          		 
     
         		 
     
     
    k
    		 
     
          		 
     
          		 
     
     




  5. Describe the effect that varying a and b in the standard equations (x - h)2/ a2 - (y - k)2/ b2 = 1 and -(x - h)2/ a2 + (y - k)2/ b2 = 1 has on the graph of a hyperbola.






  6. The equation -9x2 + y2 - 144x - 6y - 648 = 0 defines a hyperbola. Identify the centre, opening direction, vertices and the slopes of the asymptotes of this hyperbola.

    Centre: ________________     Vertices: ________________

    Opening direction:
    ________________     		    
    Slopes of Asymptotes
    ________________




  7. On the provided graph paper, sketch the graph of the hyperbola defined by the equation 64x2 - 100y2 - 6400 = 0.

  8. If the equation Ax2 + By2 + Cx + Dy + F = 0 and the equation Ax2 + By2 = P define a hyperbola, then what must be true about the values of the coefficients A and B in both equations?






  9. A hyperbola is defined by the standard equation (x - 6)2 - (y - 6)2 = 1 and by the general equation x2 - y2 - 12x + 12y - 1 = 0.
    a) Show that these equations are equivalent.






    b) When two equations are equivalent they have identical solution sets. Verify that the point (5, 6) is a solution of both equations.







  10. A hyperbola is formed when a plane cuts both naps of a double-napped cone. Describe what happens to the hyperbola as:

    a) The plane moves closer to the vertical axis.



    b) The plane moves farther away from the vertical axis.



    c) The plane cuts exactly through the vertical axis.





  11. Explain why (or show how) the horizontal and vertical axes of symmetry can be used to describe the slopes of the asymptotes as +b/a and -b/a for a hyperbola defined by (x - h)2/ a2 - (y - k)2/ b2 = 1.