9.3 Graph & Write Equations of
Circles
Algebra 2
Standard Form of the Equation of a
circle (center at origin) with radius, r
x y r
2
2
2
x  y  49
2
2
Ex. 1) Graphing an Equation of a
Circle

Draw the circle
x   y  27
2
2
Ex. 2) Graphing an Equation of a
Circle

Draw the circle
4 x  4 y  128
2
2
Ex. 3 Write the standard form of the equation
of the circle with the given radius & whose
center is the origin.
4 6
Distance formula/radius when
center is (0,0)
r  ( x  0)  ( y  0)
2
2
or
x y r
2
2
2
Ex. 4) Write an Equation of a
Circle

when (-4,7) is on a circle centered
at the origin.
To find a tangent line




1.) Find the slope of the radius
2.) Find Slope – opp. Reciprocal for
a perp. Line to the radius
3.) Use given point & new slope
from step #2 to plug into pointslope form or slope intercept form
(twice).
4.) Final equation should be in slope
intercept form.
Ex. 5) Finding a Tangent Line

Write an equation of the line that is
tangent to the circle x 2  y 2  17 at (1,4)
Using circles in real life


Region inside circle:
Region outside circle:
x y r
2
2
2
x y r
2
2
2
Ex. 6

A street light can be seen on the
ground within 30 yd of its center.
You are driving and are 10 yd east
and 25 yd south of the light.


a.) Write an inequality to describe the
region on the ground that is lit by the
light.
b.) Is the street light visible?