Download circles mini-quiz practice solutions

Advanced Math
Name _____________________________
Circles Practice Mini-Quiz
1.
2.
Find the center and radius:
( x + 3)2 + (y ! 2)2 = 7
center: (-3, 2)
radius:
7
Find the center and radius:
x 2 ! 4x + y 2 + 8y ! 2 = 0
x 2 ! 4x + 4 + y 2 + 8y +16 = 2 + 4 +16
(x ! 2)2 + (y + 4)2 = 22
center: (2, –4)
3.
radius: 22
Find the equation of a circle with endpoints of a diameter (5, 1) and (–3, 7).
" 5 + !3 1 + 7 %
,
' = (1, 4)
2
2 &
2
2
2
equation so far: (x !1) + (y ! 4) = r
(5 !1)2 + (1 ! 4)2 = r 2
center is midpoint: $
#
2
plug in a point on the circle to find r :
16 + 9 = r 2
r 2 = 25
2
replace r with 25:
4.
(x !1)2 + (y ! 4)2 = 25
Find the equation of a circle tangent to the x-axis with center (–5, 7).
Radius is 7, since center is 7 units away from x-axis.
(x + 5)2 + (y ! 7)2 = 49
5.
Find the equation of the line tangent to the circle at the point where the circle
passes through the point (–2, 5) if the circle is centered at (1, 4).
4 ! 5 !1
=
1 ! !2 3
Perpendicular:
m! = 3
Line equation: y ! 5 = 3(x + 2)
Line slope would be perpendicular to radius. Radius slope: