Determination of center and radius of circumference

Given the general equation of a circumference, we use the perfect square trinomial factorization process to transform it into the reduced equation, and thus determine the center and radius of the circumference. To do so, the general equation must meet two conditions:

  • the coefficients of the terms x2 and y2 must be equal to 1;

  • there should not be the term xy.

So let's determine the center and radius of the circle whose general equation is x2 + y2 - 6x + 2y - 6 = 0. Looking at the equation, we see that it meets both conditions. Like this:

  • Step 1: We group the terms into x and the terms in y and we isolate the term independent

x2 - 6x + _ + y2 + 2y + _ = 6

  • Step 2: We determine the terms that complete the perfect squares in the variables. x and y, adding to both members the corresponding installments

  • Step 3: We factor in the perfect square trinomials

(x - 3) 2 + (y + 1) 2 = 16

  • 4th step: obtained the reduced equation, we determine the center and the radius

Next: Position of a Point Relative to a Circle