right arrow
Examples: Monday, today, last week, Mar 26, 3/26/04
We have identified a log in issue that is preventing some members from accessing the site. The support team is diligently working on resolving it. We hope to have an update soon. Read more here. Thanks for your understanding!


Please explain, the graph of x^2=(2y+3)^2
5 replies
· Reply · Share

Replies to: Conic

  • MITer94MITer94 4728 replies19 threads Senior Member
    edited May 2015
    If x^2 = (2y+3)^2, then either x = 2y+3 or x = -(2y+3). The graph should look like two intersecting lines.
    edited May 2015
    · Reply · Share
  • bjkmombjkmom 7941 replies158 threads Senior Member
    It's been a zillion years, so someone check me on this:

    Subtract from the right, and foil it out. You get x^2 - 4y^2 -6y-9 = 0
    Add 9 to both sides.

    Complete the square for the y.

    I'm pretty sure it should be a hyperbola.

    But I haven't done conics since 2000, when I last taught Precalc. And I only have these 30 seconds before I get my kids up. So don't take my word as definite.
    · Reply · Share
  • bjkmombjkmom 7941 replies158 threads Senior Member
    Let me try again:
    FOIL the right: x^2 = 4y^2+12y + 9
    Subtract everything but the 9 from the right; x^2 - 4y^2 - 12y = 9
    Factor : x^2 -4(y^2 + 3y) = 9
    Complete the square: x^2 -4(y^2 + 3y + 9/4) = 9
    Factor: x^2 -4( y+ 3/2) ^2 = 9 + 4(9/4)
    Simplify: x^2 -4(y+ 3/2)^2 = 18
    Set right = 1 x^2 / 18 -2(y+3/2)^2 / 9 = 1

    Check my algebra... as I said, it's been a million years since I did this.
    But that should absolutely get you started. But you can now find the values of a, b and c.
    · Reply · Share
  • MITer94MITer94 4728 replies19 threads Senior Member
    @bjkmom Technically it is a degenerate hyperbola (see here) but for these purposes, the graph is simply a pair of intersecting lines.

    FYI You can always use WolframAlpha or another graphing software to graph equations such as x^2 = (2y+3)^2.
    · Reply · Share
This discussion has been closed.

Recent Activity