Question

#43 please, still checking work..... p.s. if im slow to reply i am sorry, ive been doing homework and correcting it for around 9 hours.

Answer 1

Given that:

Foci: (0,3), (0,-3)

Co-vertces: (1,0), (-1,0)

The foci are on the y-axis, so the major axis is the y-axis. Thus the equation will have the form:

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

The foci are (0,3) and (0,-3), so

`c=3\Rightarrow c^2=9`

The co-vertices are (1, 0) and (-1, 0), so

`b=1\Rightarrow b^2=1`

The co-vertices and foci are related by the equation

`c^2=a^2-b^2`

Solving for the square of a.

`\begin{gathered} 9=a^2-1 \\ a^2=10 \end{gathered}`

Substituate the obtained values into the standard form of he ellipse. Hence the equation of the ellipse is

`(x^2)/(1)+(y^2)/(10)=1`