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:

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

then, in this case,we have the following:

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

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