Answer:
- center: (2, -1)
- radius: 4
- standard form: (x -2)² +(y +1)² = 16
- general form: x² +y² -4x +2y -11 = 0
Explanation:
You want the center, radius, and equations in standard form and general form for the circle shown in the graph.
Center
The center is the point marked. Its coordinates are ...
(x, y) = (2, -1)
Radius
The radius is the distance from the center to any point on the circle. It is usually convenient to read the radius on a graph by considering points on the same horizontal or vertical line as the center of the circle.
Here, the circle passes through point (6, -1), so the radius is 6 -2 = 4.
The radius is 4 units.
Standard form
The standard form equation for a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
For center (2, -1) and radius 4, this is ...
(x -2)² +(y +1)² = 16 . . . . standard form equation
General form
The general form of a polynomial equation is f(x, y) = 0, with the terms listed in lexicographical order by decreasing degree. This is found from the standard form by expanding it, combining terms, and arranging them in the required order:
(x -2)² +(y +1)² = 16 . . . . . standard form
x² -4x +4 +y² +2y +1 -16 = 0 . . . . . eliminate parentheses, subtract 16
x² +y² -4x +2y -11 = 0 . . . . general form equation