Page 5 - For Okta_Float

a. The location of the PADS, 2 miles west and 3.5 miles south of downtown
Olympia, Washington, can be expressed as the ordered pair (2, 3.5).
Since any point 24 miles from the seismograph could be the epicenter, the
radius of the circle is 24.
2
2
(x h) (y k) r 2 Standard form
2
2
[x (2)] [y (3.5)] 24 2 (h, k) (2, 3.5) and r 24
Graphing 2 2
Calculator (x 2) (y 3.5) 576
Tip b. The location of the epicenter lies on y
To graph a circle on a the circle with equation 30
2
2
graphing calculator, first (x 2) (y 3.5) 576. 20
solve for y. Then graph
the two resulting 10
equations on the same x
screen by inserting 30 20 10 O 10 20 30
{1, 1} in front of 10
the equation for the
symbol . Use 20
5:ZSquare in the
ZOOM menu to make 30
the graph look like (x 2) (y 3.5) 576
2
2
a circle

The standard form of the equation of a circle can be expanded to obtain a
general form of the equation.
2
2
(x h) (y k) r 2 Standard form
2
2
2
2
2
2
(x 2hx h ) (y 2ky k ) r 2 Expand (x h) and (y k) .
2
2
2
2
2
x y (2h)x (2k)y (h k ) r 0
Since h, k, and r are constants, let D, E, and F equal 2h, 2k and
2
2
2
(h k ) r , respectively.
2
2
x y Dx Ey F 0
This equation is called the general form of the equation of a circle.
General The general form of the equation of a circle is
Form of 2 2
the Equation x y Dx Ey F 0,
of a Circle where D, E, and F are constants.
2
2
Notice that the coefficients of x and y in the general form must be 1. If
those coefficients are not 1, division can be used to transform the equation so
that they are 1. Also notice that there is no term containing the product of the
variables, xy.
When the equation of a circle is given in general form, it can be rewritten in
standard form by completing the square for the terms in x and the terms in y.
Lesson 10-2 Circles 625