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