Question

Identify the center and intercepts of the conic section:
Center: ( , ) x-intercepts: ( , ) y-intercepts: ( , )
( , ) ( , )
Domain_________________ range: ______________

Answer 1

@mathmale Do you mind helping me with this question?

Answer 2

Hello, Yana! I've been on Open Study most of the day and would really like to get off now. However, if you could take a screen shot of the original problem and share it with me here, I'll help you. Can you do that?

Answer 3

Based upon your own drawing, I see that the x=intercepts are (-2,0) and (4,0). Can you agree with that? The length (along the major axis) of the ellipse is then 4-(-2)=6. Half of that is 3. 3 represents the distance from the center of the ellipse to either vertex.

In other words, a=3.

Next, the distance from the center of the ellipse to the max or min y-value is 2.

In other words, b=2.

the equation of the ellipse is\[\frac{ (x-h)^2 }{ a^2}+\frac{ (y-0)^2 }{ b^2 }=1.\]

substitute your values of a and b.

Find the h, the x-coordinate of the center, and substitute that for h.

Last, to find the vert. int., let x=0 and find the 2 corresponding y-values.

Good luck, Yana!!