1. CONICS Chapter 7

2. 7.1 – Geometric Locus Definition: The set of points having a
common characteristic is
called a geometric locus
which is described by a
locus equation

3. Example 1 The set of points in the 1st quadrant
of the Cartesian plane whose
distance from the x-axis and the
y-axis are equal.
DRAW THE PICTURE!!!!

4. Example 1 Geometric locus: Bisector of the 1st quadrant
Locus Equation:
y=x (x≥0)

5. Example 2 The set of points in the Cartesian plane
located 2 units from the x-axis and
having a positive y-coordinate
DRAW THE PICTURE!!!!

6. Example 2 Geometric locus: Horizontal line through (0,2)
Locus Equation:
y=2

7. CIRCLES
Section 7.2

8. Investigation Can you find how long the radius is? c2 = a2 + b2

9. Circle – Centered at the origin
Definition:
A circle centered at the origin is the set of points M in the plane located at a constant distance from the origin. This distance is called the radius r of the circle.
The origin is called the center.
M(x,y) r

10. Circle – Centered at the origin
Standard Form Equation:
x2 + y2 = r2
Mϵ ϐ ↔ d(0,M) = r

11. Example 3 x2 + y2 = 52 x2 + y2 = 25 22 + 42 = r2 20 = r2 x2 + y2 = 20
Find the equation of the circle centered at the origin:
a) with radius 5
b) passing through (2,4)
x2 + y2 = 52
x2 + y2 = 25
= r2
20 = r2
x2 + y2 = 20

12. Circle NOT centered at the origin
Definition:
A circle centered at w is the set of points M in the plane located at a constant distance from the center (h,k).
M(x,y) r
w (h,k)

13. Circle NOT centered at the origin
Standard Form Equation:
(x-h)2 + (y-k)2 = r2
Mϵ ϐ(w,r) ↔ d(w,M) = r

14. Example 4 (x+3)2 + (y-2)2 = 52 (x+3)2 + (y-2)2 = 25
Find the equation of the circle centered at the origin:
a) with radius 5, w (-3,2)
b) passing through M(1,7), w (1,3)
(x+3)2 + (y-2)2 = 52
(x+3)2 + (y-2)2 = 25
(1-1)2 + (7-3)2 = r2
42 = 16 = r2
(x-1)2 + (y-3)2 = 16

15. SHOW ME YOU SIGNED TESTS
HOMEWORK
WORKBOOK
p. 322 #1
p. 323 #1,2,3,4
p. 324 Activity 2 a)
p. 325 #5,6,7,8,9
SHOW ME YOU SIGNED TESTS