A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

how to find the center and radius of x^2+y^2-x+2y+1=0?

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

    centre at: \( (\frac 12,-1) \)

  2. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    radius is \(\frac 12 \) units.

  3. xkehaulanix
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    FoolForMath is right (I think). You have to get the problem into a form you can recognize. The equation for a circle is \[(x - a)^2 + (y - b)^2 = r^2\] Start by separating your equation by variables and the constant (1): \[x^2 - x + y^2 + 2y = -1\] To factor the x and y terms, you need to finish the squares. Simplest way to do so is divide the non-squared x and y terms' coefficients (-1 and 2) by 2 and square them. (-1/2)^2 = 1/4 (2/2)^2 = 1 Then add these into the equation-both sides of it to keep it balanced:\[x^2 - x + 1/4 + y^2 - 2y + 1 = -1 + 1/4 + 1\]Then simplify.\[x^2 - x + 1/4 + y^2 + 2y + 1 = 1/4\]Complete the squares on the left side of the equation (factor them): \[(x - 1/2)^2 + (y + 1)^2 = 1/4\]The radius is of the form (a, b), which in this case is (1/2, -1). The radius is the square root of the right side of the equation, which in this case is 1/2.

  4. 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.