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: Standard form of an ellipse

  1. Mar 26, 2005 #1
    When in standard form how do you know whether the ellipse is horizontal or vertical? and how do you know what a= and b= for the major and minor axis, and vertices? How do you get the coordinates of the foci?
  2. jcsd
  3. Mar 26, 2005 #2
    If the denominator attached to the x is less than that of the y then it will be vertical, (as there is less of a distance between the x intercepts that the y).

    The semi-major axis will be the root of the largests denominator
    The semi-minor axis will be the root of the smallest denominator
    The coordinates of the center will be (h,k) for and elispse in the form (just a simple translation)

    [tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2}=1[/tex]
  4. Mar 26, 2005 #3
    how about the coordinates of the foci?
  5. Mar 26, 2005 #4


    User Avatar
    Science Advisor
    Homework Helper

    If you know what's special about the covertex, there's a very easy way to find the coordinates of each focus.

    Both focii lie on the major axis. For a horizontal ellipse, your coordinates have to be (x,0). For a vertical ellipse, (0,y).

    The covertex is the point where the minor axis intersects the ellipse. Half of the minor axis is the semi-minor axis (b) and half of the major axis is the semi-major axis (a). The distance from either focus to the covertex is equal to the semi-major axis.

    Now you know two sides of your triangle. You know the hypotenuse which happens to have a length equal to the semi-major axis (a). You know the semi-minor axis (b) which forms one leg of your triangle. You also know the minor axis is perpendicular to the major axis, so you know you have a right triangle.

    You use the Pythagorean thereom to find the missing length: the length from your origin to the focus. The length will be equal to your linear eccentricity (c). In other words, you have [tex]a^2=b^2+c^2[/tex]. For a horizontal ellipse, the length is the missing x variable in your coordinates. For a vertical ellipse, the missing y variable. For the opposite focii, just reverse the sign (positive x to negative x, pos y to neg y, as applicable).
  6. Mar 26, 2005 #5
    lol woh bob u got way too complicated how did triangles get into this :rofl:
  7. Mar 26, 2005 #6


    User Avatar
    Science Advisor
    Homework Helper

    Maybe a drawing would help. I drew a horizontal ellipse, where the major axis lies along the x-axis. The coordinates of your focii would be (c,0) and (-c,0)

    Attached Files:

  8. Mar 26, 2005 #7
    how do I open the attachment?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook