1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: System of equations with 2 parameters

  1. Jun 2, 2013 #1
    1. The problem statement, all variables and given/known data
    I have a system of two equations:

    3*x^2 - x + 3*y^2 = 0
    2*x^2 - y + 2*y^2 = 0

    2. Relevant equations

    3. The attempt at a solution
    I don't know how to express one with the other.I mean I can either have x = 3*y^2 + 3*x^2 or y = y = -2*y^2 - 2*x^2 and in both cases it becomes an utter mess.What can I do?
  2. jcsd
  3. Jun 2, 2013 #2


    User Avatar
    2017 Award

    Staff: Mentor

    I would modify the second equation to get x^2 = ... and therefore x = ... and use this in the first equation.
  4. Jun 2, 2013 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Here's another suggestion. You can see by inspection that (0,0) is one intersection point. Since both equations represent circles, put them in standard form and locate their centers. Determine the slope ##m_1## of the line of centers. The slope of the common chord between their intersection points will be ##m_2=-\frac 1 {m_1}##. The line through the origin with that slope ##m_2## whose equation is ##y=m_2x## will pass through the other intersection point. Solve that with one of your circles. It works out pretty easily.
  5. Jun 3, 2013 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    One more suggestion: can you spot a multiplier that makes the quadratic terms in one equation the same as those in the other?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted