A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

A circle has the same center point as an ellipse whose equation is 32x^2+18y^2-128x-180y+290=0.If the circle just fits inside ellipse,what is the diameter of the circle?

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Keep in mind a circle is really just an ellipse with major and minor axes being the same length. An ellipse is really just a stretched out circle in one direction, so we want to find the length of the minor axis of the ellipse and that will be our diameter. A bit of rearranging... 32x^2 - 128x + 18y^2 - 180y = -290 16x^2 - 64x + 9y^2 - 90y = -145 16(x^2 - 4x + ______) + 9(y^2 - 10y + ______) = -145 + ______ + ______ Complete the square: 16(x^2 - 4x + 4) + 9(y^2 - 10y + 25) = -145 + 64 + 225 16(x - 2)^2 + 9(y - 5)^2 = 144 \[(x - 2)^2/9+(y -5)^2/16 = 1\] From our ellipse equation, we can see that our a^2 = 9 --> a = 3. Now, this is only one half of the minor axis, so we only have the radius of the circle. The diameter is 2*3 = 6.

  2. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.