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Find an ellipse centered through the origin that runs through 3 points

  1. Apr 11, 2013 #1
    Find the ellipse centered at the origin that runs through
    the points (1,2), (2,2), and (3, I). Write your equation
    in the form $$ ax^2 + bxy + cy^2 = 1 $$

    I understand the $$ ax^2 $$ and $$ cy^2 $$ in the equation because the equation of an ellipse centered at origin is $$ (x/a)^2 + (y/b)^2 = 1 $$ so we let $$ a = (1/a)^2 $$ and $$ b = (1/b)^2 $$. but where did the $$ bxy $$ come from?
     
  2. jcsd
  3. Apr 11, 2013 #2

    Dick

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    ##(x/a)^2 + (y/b)^2 = 1## is only the equation of an ellipse centered at the origin whose axes are parallel to x and y axes. ##ax^2 + bxy + cy^2 = 1## is more general. It may be at an angle. Just put the given values for x and y in and get three equations to solve for the three unknowns a, b and c.
     
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