Standard Form to General Form of a Circle Calculator

Created by Vishnuvardhan Shakthibala
Reviewed by Krishna Nelaturu
Last updated: Nov 10, 2022

If you're looking for a quick way to convert the circle equation from standard form to general form, our standard form to general form of a circle calculator is a perfect match for you.

Please read this short article to learn more about:

  • How to use our standard form to the general form of a circle calculator?; and
  • How to convert the circle equation from standard form to general form?

How to use our standard form to general form of a circle calculator?

To use our calculator, you can use the following guide:

  • Make sure your circle equation is in standard form: (xh)2+(yk)2=C(x-h)^2 +(y-k)^2=\text{C};
  • Insert the parameters: h, k, and C present in standard form into the respective fields; and
  • Right away, you will get the circle equation in a general form.

Nice, you are an expert in using our calculator now ;).

How to convert the circle equation in standard form to general form ?

To convert the circle equation from the standard to general form, you can use the following steps:

  1. Extract the radius and center information from the standard form. You can see below from the standard form we can observe the variables h, and k, which correspond to the center, and r corresponds to the radius.
(xh)2+(yk)2=r2\qquad \footnotesize (x-h)^2 +(y-k)^2=r^2
  1. General form of the circle equation is given as:
x2+y2+Dx+Ey+F=0\qquad \footnotesize x^2 +y^2+Dx+Ey+F=0
  1. Now, use the following formula to compute the coefficients of the general form:
D=2×hE=2×kF=h2+k2r2.\qquad\footnotesize \begin{align*} D&=-2×h\\ E&=-2×k \\ F&=h^2+k^2-r^2. \end{align*}
  1. Finally, substitute the values obtained to get the circle equation in a general form.

Excellent, you have learned how to convert circle equation from standard form to general form.

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FAQ

What is the general form of a circle equation with diameter endpoints (4,8), (6,6)?

The general form is given as x²+y²-10x-14y+72=0. To find the general form, start with the general form x²+y²+Dx+Ey+F=0, and let's find the coefficients using the following steps:

  1. Find the center (h,k) and distance between the diameter endpoints using the midpoint and distance formulas, respectively.
  2. Divide the distance found in step 1 by 2 to obtain the radius r=1.4142.
  3. Calculate the coefficients of the general form using the following equation:
    D=-2×h=-10;
    E=-2×k=-14; and
    F=h²+k²-r²=72.
  4. substitute the coefficients to obtain the circle equation in a general form:
    x²+y²-10x-14y+72=0

How do I find the radius from circle equation in general form?

To find the radius from the general form, use the following steps:

  1. Extract the coefficients from the general form: x²+y²+Dx+Ey+F=0;
  2. Use the formula of F which is given as F=(D/2)²+(E/2)²-r².
  3. Rearrange the formula of F in terms of radius r: r=√((D/2)²+(E/2)²-F); and
  4. Solve the equation in step 3 to obtain the radius of the circle.

Hooray! Now you know how to find the radius if you are given with circle equation in a general form.

Vishnuvardhan Shakthibala
Standard form: (x - h)² + (y - k)² = C
h
k
C
General form: x² + y² + Dx + Ey + F = 0
D
E
F
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