Math 1119

Review

Test 4

  1. Find the vertices, foci and eccentricity of the ellipse given by .  Determine the lengths of the major and minor axes, and sketch the graph.

 

  1. Find the equation of an ellipse with endpoints of the major axis at (13, 1), and       (-5, 1), and a distance of 6 between the foci.         

 

  1. Find the focus, directrix, and length of the focal diameter for

 

  1. Sketch the graph of .

 

  1. Find the equation of the parabola with horizontal axis and vertex at the origin that passes through (-2, 5).           

 

  1. Find the equation of the hyperbola with asymptotes y = 2x+1 and y = -2x -1 and has a major axis going horizontally of length 6.
  2. Find the vertices, foci and asymptotes of the hyperbola.  Then sketch the graph.
  3. Complete the square to determine whether the following equation represents a parabola, ellipse, hyperbola or degenerate conic.  Then sketch the graph of the equation.                                                                     

 

  1. Determine the XY coordinates of (3,- 2) if the axis is rotated through. 

 

  1. Given the following equation:
    1. Determine the angle that you would rotate the axis through to eliminate the xy-term.                                                                               
    2. Use the discriminant to determine if the above equation is a parabola, ellipse, or hyperbola.                                                                   
  2. Sketch the parametric curve defined by
  3. Find the rectangular coordinate equation for the parametric curve above.

 

  1. An archer shoots an arrow from a height of 5 feet at an angle of elevation of  with a velocity of 250 feet per second.                                               
    1. Write a parametric equation for the path of the arrow.

 

    1. What will be the maximum height of the arrow?

 

    1. How long will it take for the arrow to hit the ground?

 

    1. How far will the arrow travel before it hits the ground?  Round to the nearest foot.

 

    1. A deer is 100 yards away from the archer.  Will he/she hit the deer?  It’s body is from 3 to 4.5 feet high.

 

  1. Express the vector with initial point (-2, 7) and terminal point (1, 2) in component form.

 

  1. Determine the magnitude of the vector u = 5i - 2j.

 

Given: u = i + 2j and v = 5i – 3j:

  1. Find                                

 

  1. u + v

 

  1. 3u

 

  1. Determine the angle between u and v.              

 

  1. A plane is headed in a direction 60 degrees east of north with a velocity of 500 mph.  The effect of the wind is 25 mph in a direction 45 degrees south of north.  What will be the true velocity and heading of the plane?   

 

  1. Vectors pushing a car up a hill.

 

  1. Vectors and force components for a hanging object.

 

 

 

 

 

 

  1. Sketch the graph of                                              

 

 

  1. Sketch the graph of r = 4 – 3cos.      

                                   

  1. Sketch the graph of r = 4 + 5cos.                                         

 

 

 

 

  1. Sketch the graph of r = 2+2cos.                                           

 

 

25.       You should be able to find the polar equation given its graph.