Question
upstudy study bank question image url

Write the equation of the circle centered at \( (-8,6) \) with diameter 16 . Question Help: Video \( \square \) Message instructor Submit Question Jump to Answer

Ask by Cole Romero. in Canada
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The equation of the circle is \( (x + 8)^2 + (y - 6)^2 = 64 \).

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Beyond the Answer

The equation of a circle is given by \( (x - h)^2 + (y - k)^2 = r^2 \), where \( (h, k) \) is the center of the circle and \( r \) is the radius. Since the center is \( (-8,6) \) and the diameter is 16, the radius \( r \) will be half of that, which is 8. Therefore, the equation becomes: \[ (x + 8)^2 + (y - 6)^2 = 8^2 \] or \[ (x + 8)^2 + (y - 6)^2 = 64. \] Circles have been studied since ancient times, first by Greeks who found their perfect shapes fascinating. They reflected harmony and beauty in art and architecture. Fast forward to today, the circle serves a vital role in various fields, from physics using circular motion concepts to computer graphics utilizing circular objects for design. It's fascinating how this simple shape has transcended time and discipline! When working with the circle's equation, a common mistake is confusing the diameter with the radius. Remember, the radius is always half of the diameter! Also, while plotting, ensure you center your coordinate axes correctly to avoid skewing the circle's true placement. Keep those coordinates in check to show off that perfect round shape!

Related Questions

Latest Geometry Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy