General Form of the Equation

Key Questions

  • How do I find the radius of a circle from its general equation?

    The general form of a circle looks like ...

    #x^2+y^2+Ax+By+C=0#

    In the standard form to the equation for a circle look like ...

    #(x-h)^2+(y-k)^2=r^2#

    #sqrt(r^2)=r,#radius

    Convert the general form to standard form by using the completing the square process.

    You will then have the #r^2# value.

    The square root of #r^2# is the radius of the circle.

    AJ Speller · 1 · Sep 14 2014
  • How can a general equation tell me whether a conic section is a circle or an ellipse?

    General equation of ellipse or circle

    #(x-h)^2/a^2+(y-k)^2/b^2=1#

    If #a=b# then you have a circle.

    If #a>b# then you have an ellipse where the #x# axis is the major axis.

    If #b>a# then you have an ellipse where the #y# axis is the major axis.

    AJ Speller · · Sep 14 2014
  • How can I tell whether an ellipse is a circle from its general equation?

    Answer:

    A circle in general form has the same non-zero coefficients for the #x^2# and the #y^2# terms. So if there is a graph, it is a circle (or a point).

    Explanation:

    Don't be too hasty, though.

    #Ax^2+Bxy+Cy^2+Dx+Ey+F=0#

    Assuming that there is ineed a graph, it is:

    an ellipse if #A# and #C# have the same sign.

    a circle if #A=C#.

    However it is possible that there is no graph:

    #x^2+y^2=-9/4# Has no graph, but it can be rewritten as:

    #4x^2+4y^2+9=0#. At first look, this appears to be the equation of a circle, but it is not.

    Jim H · 1 · Jul 16 2015

Questions

Geometry of an Ellipse