Circle Equation Converter: Standard to General Form Calculator
Overview: This free online calculator efficiently converts a circle's equation from standard to general form. Input the parameters h, k, and C (or r²) from the standard form (x−h)²+(y−k)²=C, and it instantly provides the equivalent general form x²+y²+Dx+Ey+F=0. This guide also explains the manual conversion formulas.
How to Use the Standard to General Form Calculator
Using this tool is straightforward for quick results.
- Ensure your circle equation is in the correct standard form:
(x−h)² + (y−k)² = C. - Input the values for parameters h, k, and C into the designated fields.
- The calculator will immediately generate and display the corresponding general form equation.
Manual Conversion from Standard to General Form
Understanding the manual process empowers you to solve problems independently. Follow these steps.
Begin by extracting the center (h, k) and radius r from the standard form: (x−h)² + (y−k)² = r².
The key conversion formulas are:
D = -2h
E = -2k
F = h² + k² - r²Finally, substitute the computed values for D, E, and F into the general form structure: x² + y² + Dx + Ey + F = 0.
Frequently Asked Questions
What is the general form for a circle with diameter endpoints at (4,8) and (6,6)?
To find the general form, first calculate the center (midpoint) and radius from the endpoints. The center (h, k) is ((4+6)/2, (8+6)/2) = (5, 7). The radius r is half the distance between the endpoints. Then, apply the formulas D = -2h, E = -2k, and F = h² + k² - r² to get the coefficients for the general form.
How can I determine the radius from an equation in general form?
Given the general form x² + y² + Dx + Ey + F = 0, you can find the radius using the rearranged formula:
r = √( (D/2)² + (E/2)² - F )Extract the coefficients D, E, and F from your equation and insert them into this formula to solve for the radius r.