1. Precalculus – 2015
circle

2. The set of all points satisfying the equation gives x -4 4 8 r
height = y-k
Base = x-h
Pythagorean Theorem?
The set of all points satisfying the equation gives
the circle with center (h,k) and radius = r .

3. Circle
The set of all co-planar points equidistant from a fixed point (center).
radius

4. Circle
Equation: (x – h)2 + (y – k)2 = r2 r
(h, k)

5. Circle r = r = 11 x – 3 = 0 x = 3 y – 5 = 0 y = 5 121 11 (3, 5) center

6. Circle r = r = 9 x + 5 = 0 x = -5 y – 2 = 0 y = 2 81 9 (-5, 2) center

7. Graph the following circle
9x2 + 36x + 9y2 - 18y - 10 = 89
9x2 + 36x + 9y2 - 18y =
9x2 + 36x + 9y2 - 18y = 99 9
(x2 + 4x + 22 ) + (y2 - 2y + (-1)2 ) =
(x + 2)2 + (y - 1)2 = 16

8. Circle r = r = 4 x + 2 = 0 x = -2 y – 1 = 0 y = 1 16 4 (-2, 1) center

9. Graph the following circle
4x2 + 24x + 4y2 + 32y + 13 = 157
4x2 + 24x + 4y2 + 32y =
4x2 + 24x + 4y2 + 32y = 144 4
(x2 + 6x + 32 ) + (y2 + 8y + 42 ) =
(x + 3)2 + (y + 4)2 = 61

10. Circle r = x + 3 = 0 x = -3 y + 4 = 0 y = -4 61 61 (-3, -4) center

11. Graph the following circle
5x2 - 80x + 5y2 + 20y - 34 = 106
5x2 - 80x + 5y2 + 20y =
5x2 - 80x + 5y2 + 20y = 140 5
(x2 - 16x + (-8)2 ) + (y2 + 4y + 22 ) =
(x - 8)2 + (y + 2)2 = 96

12. Circle r = r = 4 6 x - 8 = 0 x = 8 y + 2 = 0 y = -2 96 4 6 (8, -2)
4 6
y + 2 = 0
(8, -2)
y = -2
center
(8, -2)

13. Graph the following circle
2x2 + 10x + 2y2 + 8y + 4 = 25
2x2 + 10x + 2y2 + 8y =
2x2 + 10x + 2y2 + 8y = 21 2
(x2 + 5x ) + (y2 + 4y + 22 ) =
(x + )2 + (y + 2)2 =

14. Circle r = r = x + = 0 x = y + 2 = 0 y = -2 center

15. Circles
Find the equation of a circle where the endpoints of a diameter are
(-5,-7) and(-5,11)

16. Circles
Find the equation of a circle where the endpoints of a diameter are
(-4,-6) and(2,2)

17. Circles
Find the standard form of the equation of a circle that contains the points (9,4), (1,14) and (9,14).
Use the idea that the perpendicular bisector of any chord of a circle passes through the center of the circle. Since the given points are on the circle, any pair of the three points are the endpoints of a line segment that is a chord of the circle.
Find the perpendicular bisector of 2 of the chords. Their intersection will be the center of the circle. Distance from center to any of the points = radius.

19. ♫
Happy Pi-Day
March 14

20. Homework:
Circles Worksheet