Question

Write the equation of an ellipse with intercepts (-2,0), (2,0), (0,4), (0,-4). Then find the foci. Write the answer as square root (No decimals) Show work.

Answer 1

First, the major axis of the ellipse is vertical. The standard form of the equation of a vertical ellipse is
`(x^2)/(b^2)+(y^2)/(a^2)=1`. Here we can see that
`b=2` and
`a=4`. So the equation is
`(x^2)/(4)+(y^2)/(16)=1`. To find the foci, use
`c^2=a^2-b^2= 16-4\\ \implies c=√(12)=2√(3)`. The foci will be located on the axis the vertexes are on, so that makes the coordinates of the foci
`(0,\pm 2√(3))`.