Precalculus H/GT
Worksheet: Conics – Circles
Write an equation in standard form of each circle described below:
1. End points of a diameter are (3, 2) and (5, –4).
2. r  5 , Center (-3, 5)
3. r  8 , Center (-1, -6)
4. r  12 , Center (4, -2)
5. r  12 , Center ( 12 , 0)
Find the center, radius, and area of each circle:
6.
 x  4   y  6
2
2
 18
7. 3  x  4   3 y 2  54
2
8. x 2  y 2  4 y  0
9. x 2  y 2  2 x  4 y  4  0
10. 2 x 2  2 y 2  2 x  y  0
11. Find the equation in general form of the circle with center (3, 5) and tangent to the x-axis.
12. Find the equation of the circle having center (2, -3) and radius 6.
13. Find the equation of the circle having center (2, -3) and passing through the point (-4, 2).
14. Find the equation of the circle having center on the line x  y  5 and tangent to the x-axis at
the point (8, 0).
15. Find the equation of the line that is tangent to the circle x 2  y 2  34 at point (3, 5).
16. Find the equation of the line that is tangent to the circle x 2  y 2  8 x  12 y  42  0 at (5, -3).
Answer List:
1.
 x  4   y  1
2.
 x  3   y  5
3.
 x  1   y  6
4.
 x  4   y  2
2
2
2
2
2
 10
2
 25
2
 64
2

1
4
2
1
1

5.  x    y 2 
2
4

6. r  3 2, C  4,6 , A  18
7. r  3 2, C  4,0 , A  18
8. r  2, C  0, 2 , A  4
9. r  3, C 1, 2 , A  9
10. r 
5  1 1
5
, C   , , A 
4
16
 2 4
11. x 2  y 2  6 x  10 y  9  0
12.  x  2   y  3  36
2
2
13.  x  2   y  3  61
2
2
14.  x  8   y  3  9
2
2
15. 3x  5 y  34  0 (Hint: the tangent line is perpendicular to the radius at the point of tangency)
16. x  3 y  4  0