what is the equation of the ellipse with co-vertices (0,2)(0,-2) and vertices (3,0)(-3,0)???

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baxthum8 | High School Teacher | (Level 3) Associate Educator

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The standard equation for an ellipse is:  `(x-h)^2/(b^2) + (y-k)^2/a^2 =1`

where a > b.

If you graph the given vertices, you will see the center is ( 0,0 ).  This means (h, k) = ( 0, 0 ).  h = 0, k = 0.  Plug these into the equation.

`(x-0)^2/b^2 + (y-0)^2/a^2 = 1`

`x^2/b^2 + y^2/a^2 = 1`

From the graph of the vertices, you notice that the distance from the center to the vertices is 3.  This means that a = 3.

From the graph of the vertices, you notice that the distance from the center to the co-vertices is 2.  This means that b = 2.  Plug these (a and b) into the equation.

`x^2/b^2 + y^2/a^2 = 1` `rArr` `x^2/2^2 + y^2/3^2 = 1` `rArr` `x^2/4 + y^2/9 = 1`

Thus your equation is:

`x^2/4 + y^2/9 = 1`

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