equation of ellipses

Question

I was given the points (1,0) (-1,0) (0,4) (0,-4) and i have to fins the equation.

Answer 1

 

When plotting the points, it is clear that the major axis for this ellipse is the 1 axis.

It is also clear that the center is (0,0)

 

The base equation for and ellipse with y axis major, and center at the origin is

 

   x²/b² + y²/a² = 1

 

   a = distance from center to a major axis vertex.  The distance from the origin to (0,4), is 4

   a = 4

 

   b = distance from center to a minor axis vertex.  The distance fro the origin to (1,0), is 1

   b = 1

 

Thus, the equation of the ellipse is:

 

    x²/1²+ y²/4² = 1