Equation of the Circle

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 1, Section 1.4

Write the standard form of the equation of the circle and the general form of the equation of the circle of radius r and center (h, k). Graph the circle.

12. r = 3; (h, k) = (0, 0)

[Math Tutor]

This one is about as friendly as they get, since the center is the origin.

Start from the standard form [tex](x - h)^2 + (y - k)^2 = r^2[/tex] and substitute [tex]h = 0[/tex], [tex]k = 0[/tex], [tex]r = 3[/tex]:

[tex](x - 0)^2 + (y - 0)^2 = 3^2[/tex]

Standard form: [tex]x^2 + y^2 = 9[/tex]

For the general form you just move everything to one side (general form is [tex]x^2 + y^2 + Dx + Ey + F = 0[/tex]):

General form: [tex]x^2 + y^2 - 9 = 0[/tex]

Here [tex]D = 0[/tex] and [tex]E = 0[/tex], which is exactly what you would expect since there is no shift away from the origin.

For the graph, put your compass point at the origin and swing a radius of 3. It crosses the axes at [tex](3, 0)[/tex], [tex](-3, 0)[/tex], [tex](0, 3)[/tex] and [tex](0, -3)[/tex], one point in each direction.