Homework- Circles
Math 120/121
Directions for problems 1-6:
1) For numbers 1-3) Put the equation into standard form for a circle by completing the
square. For numbers 4-6) Write the equation of the circle in standard form.
2) State the center and radius of the circle. Express the center as an ordered pair. If the
equation does not graph as a circle, explain why.
3) Find the x and y intercepts of the circle. Express each intercept as an ordered pair.
a) first, express each intercept in simplified radical form.
b) second, express each intercept rounded to one decimal place if necessary
4) On graph paper, carefully sketch the circle.
1) x 2  y 2  4 x  4 y  1  0
2) 2 x 2  2 y 2  12 x  8 y  24  0
3) x 2  y 2  6 x  2 y  12  0
4) Center at  2,3 and tangent to the x axis
5) Center at 1,0  and containing the point  3, 2 
6) Endpoints of a diameter at 1, 4  and  3, 2 
For problems 7 and 8: Write the equation of the circle that meets the stated conditions.
7) Center at (-2,-3) and tangent to the line y  2 x  13 (Hint: the line joining the center
of the circle and the point of tangency is perpendicular to the tangent line at the
point of tangency.)
8) Center at (11,4) and tangent to the circle ( x  2)2  ( y  1)2  10 (Hint: the centers of
both of the circles and the point of tangency lie on a single line.)
Answers
1)
( x  2)2  ( y  2)2  9 , Center at  2, 2  , radius =3


y intercepts  0, 2  5  or  0,4.2 
x intercepts 2  5, 0 or  0.2, 0  and
2)
and
 2  5, 0 or  4.2, 0
 0, 2  5  or 0, 0.2
( x  3)2  ( y  2)2  25 , Center at  3, 2  , radius =5


x intercepts 3  21, 0 or  7.6, 0  and
y intercepts
 0, 2 
and
3 

21, 0 or  1.6, 0 
 0, 6
3)
( x  3)2  ( y  1)2  2 Not a circle because r 2 is negative
4)
( x  2)2  ( y  3)2  9 , Center at  2,3 , radius =3
x intercept
y intercepts
5)
 2,0
 0,3  5  or  0,5.2
and
 0,3  5  or  0, 0.8
( x  1)2  y 2  20 , Center at 1,0  , radius = 2 5 or 4.5

y intercepts  0,



x intercepts 1  2 5, 0 or  5.5, 0  and 1  2 5, 0 or  3.5, 0 
6)

19 or  0,4.4  and
 0,  19  or  0, 4.4
( x  1)2  ( y  3)2  5 , Center at  1,3 , radius = 5 or 2.2
no x intercepts
y intercepts  0,5 and  0,1
7) ( x  2)2  ( y  3)2  80
8) ( x  11)2  ( y  4)2  40