Graph the circle expr(["+", "x^2", "y^2",
D === 0 ? null : ["*", D, "x"],
E === 0 ? null : ["*", E, "y"],
F === 0 ? null : F])
= 0.
First, convert the equation to standard form by completing the square.
Group the \blue{x} and
\green{y} terms on the left side and
move the constant term to the right side.
\qquad
\blue{
(expr(["+", "x^2", ["*", D, "x"]]))
(x^2)
} +
\green{
(expr(["+", "y^2", ["*", E, "y"]]))
(y^2)
}
\quad = \quad -F
Add
\blue{H * H} to both
sides to complete the square for the
\blue{x} term and
\green{K * K} to both
sides to complete the square for the
\green{y} term.
\qquad
\blue{
(
expr(["+", "x^2", ["*", D, "x"], H * H])
)
(x^2)
}
+ \green{
(
expr(["+", "y^2", ["*", E, "y"], K * K])
)
(y^2)
} \quad = \quad -F
+ \blue{H * H}
+ \green{K * K}
Simplify and write each term as a square:
\qquad
\blue{X2T} + \green{Y2T}
\quad = \quad R * R
\qquad
(x - \blue{negParens(H)})^2 + (y -
\green{negParens(K)})^2 \quad = \quad
\pink{R}^2
The equation of a circle with center
(\blue{h}, \green{k}) and radius
\pink{r} is
(x - \blue{h})^2 + (y - \green{k})^2 =
\pink{r}^2.
Thus, the center of the circle should be
(\blue{H}, \green{K})
and the radius should be
\pink{R}.