Question

Find the vertices and foci of the conic section \left(\frac{x}{8}\right)^2 + \left(\frac{y}{4}\right)^2 = 1 The foci are at $F_1 = \boxed{\hspace{0.5cm}}\boxed{\hspace{0.5cm}}$ (left) and $F_2 = \boxed{\hspace{0.5cm}}\boxed{\hspace{0.5cm}}$ (right) The vertices are: $\boxed{\hspace{0.5cm}}\boxed{\hspace{0.5cm}}$ (on the positive y-axis). $\boxed{\hspace{0.5cm}}\boxed{\hspace{0.5cm}}$ (negative y-axis), $\boxed{\hspace{0.5cm}}\boxed{\hspace{0.5cm}}$ (positive x-axis), $\boxed{\hspace{0.5cm}}\boxed{\hspace{0.5cm}}$ (negative x-axis).

          Find the vertices and foci of the conic section \left(\frac{x}{8}\right)^2 + \left(\frac{y}{4}\right)^2 = 1
The foci are at $F_1 = \boxed{\hspace{0.5cm}}\boxed{\hspace{0.5cm}}$ (left) and $F_2 = \boxed{\hspace{0.5cm}}\boxed{\hspace{0.5cm}}$ (right)
The vertices are:
$\boxed{\hspace{0.5cm}}\boxed{\hspace{0.5cm}}$ (on the positive y-axis).
$\boxed{\hspace{0.5cm}}\boxed{\hspace{0.5cm}}$ (negative y-axis),
$\boxed{\hspace{0.5cm}}\boxed{\hspace{0.5cm}}$ (positive x-axis),
$\boxed{\hspace{0.5cm}}\boxed{\hspace{0.5cm}}$ (negative x-axis).

Show more…

Find the vertices and foci of the conic section ((x)/(8))^2 + ((y)/(4))^2 = 1
The foci are at F1 = (left) and F2 = (right)
The vertices are:
(on the positive y-axis).
(negative y-axis),
(positive x-axis),
(negative x-axis).

Added by Monica B.

Precalculus with Limits

Ron Larson 2nd Edition

Thanks for your feedback!

Find the vertices and foci of the conic section. The foci are at F=(0, Â±âˆš6). The vertices are: (0, Â±âˆš6) (on the positive y-axis) and (0, 0) (on the negative y-axis).

Play audio

Feedback

Powered by NumerAI

Nathalie Luna and 100 other subject Precalculus educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 So in this problem, we are given this information and we are asked to find the standard form of the equation for the ellipse.

00:12 So let's see what information we do have and go from here.

00:20 Since this is, these are the two points, the coordinates for the two fulci.

00:27 So and we know that fokai are have coordinates zero plus and minus a number c.

00:39 So in this case we have c is equal to four.

00:47 And we also know that c has this formula.

00:57 That is how it is defined.

01:03 And that is on all the information that we get from here.

01:09 And as for the vertices, so since both the foci are in the x -axis, that means that this is the focal axis.

01:43 So, so the vertis these vertices, are also in the x -axis, which means that these vertices are, let's write that this way.

02:05 These vertices have coordinates zero and plus and minus a, number a.

02:14 All right, so since we have here that a is 5, that means we already know who this is.

02:30 Great.

02:31 So we have, oops, we have a squared equal to a equal to 5.

02:47 And a squared equal to 25.

03:00 This is the first thing we need for the standard form.

03:03 The other thing we need is b squared...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later