Question

fill in the blank so that the resulting statement is true. the equation ( x^{2}+y^{2}+dx + ey+f = 0 ) is called the ____ form of the equation of a circle. the equation ( x^{2}+y^{2}+dx + ey+f = 0 ) is called the form of the equation of a circle.

Explanation:

The general form of the equation of a circle is \(x^{2}+y^{2}+Dx + Ey+F = 0\). This form is different from the standard form \((x - h)^{2}+(y - k)^{2}=r^{2}\) (where \((h,k)\) is the center and \(r\) is the radius). In the general form, we can complete the square to convert it to the standard form. For example, for the equation \(x^{2}+y^{2}+2x - 4y - 4=0\), we complete the square for \(x\) and \(y\) terms: \((x^{2}+2x)+(y^{2}-4y)=4\), then \((x + 1)^{2}-1+(y - 2)^{2}-4 = 4\), and finally \((x + 1)^{2}+(y - 2)^{2}=9\).

Answer:

general