Question

3. Write an equation in standard form of an ellipse that has a vertex at (2,0), a co-Vertex at (0, 1), and a center at the origin.1O02

Answer 1

We have that the vertex is (2,0) and the co vertex is (0,1). Since the center is at the origin, we have the following:

`\begin{gathered} (h,k)=(0,0) \\ a=2 \\ b=1 \end{gathered}`

then, the standard form of the equation of the ellipse is:

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

then, in this case,we have the following:

`\begin{gathered} ((x-0)^2)/((2)^2)+((y-0)^2)/((1)^2)=1 \\ \Rightarrow(x^2)/(4)+y^2=1 \end{gathered}`

therefore, the equation of the ellipse is x^2 /4 +y^2 = 1