Circle

Generally we have the equation of circle as "  x^2 + y^2 = a^2  "whose center lies at Origin and radius is given by a.

This formula basically comes from distance formula.

If the same equation comes in modified form than we should proceed by making it look similar to standard form.

Example 5  Graph .

Solution

To determine just what kind of graph we’ve got here we need to complete the square on both the x and the y.

Recall that to complete the square we take the half of the coefficient of the x (or the y), square this and then add and subtract it to the equation.

Upon doing this we see that we have a circle and it’s now written in standard form.

                                                        

When circles are in this form we can easily identify the center : (h, k) and radius : r.  Once we have these we can graph the circle simply by starting at the center and moving right, left, up and down by r to get the rightmost, leftmost, top most and bottom most points respectively.

Our circle has a center at (-1, 4) and a radius of 3.  Here’s a sketch of this circle.