Circles

Standard form (x – h)^2 + (y – k )^2 = r^2

Where (h,k) is the center and r is the radius

You can find the radius using the distance formula with the center

and a point on the outside or you can half the diameter found by

using 2 points on the outside through the center

Equations must be put in standard form by completing the square

a. Divide by leading coefficient, move all numbers to the right

b. Half the middle term, then square it and add to both sides

c. Factor

To graph in your calculator you must solve for y and put +

and – in formula in y =

To find the intersection of a line and circle solve the line for y

Plug into the circle equation for y

Solve the quadratic

Ex 1. Find the center and radius of (x – 3)^2 + (y + 7)^2 = 19

Center: (3, 7) Radius: sqrt19

Ex 2. Given C(-1, 7) and the radius is 7 units, find the equation

of the circle in standard form.

(x + 1)^2 + (y – 7)^2 = 49

Ex 3. Find the center and radius of x^2 – 2x + y^2 – 6y = 9

-2/2 = (-1)^2 = 1 -6/2 = (-3)^2 = 9 9 + 1 + 9 = 19

(x – 1)^2 + (y – 3)^2 = 19

Center: (1, 3) Radius: sqrt19