CONICS Chapter 7

1
CONICSChapter 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 yx (x0)
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 y2
7
CIRCLES

• Section 7.2

8
Investigation
radius
Can you find how long the radius is? c2 a2
b2 r2 22 22 r2 8 r v8 r 2.82
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 M? ? ?
d(0,M) r
11
Example 3
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
22 42 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 M?
?(w,r) ? d(w,M) r
14
Example 4
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)
(x3)2 (y-2)2 52 (x3)2 (y-2)2 25
(1-1)2 (7-3)2 r2 42 16 r2 (x-1)2 (y-3)2
16
15
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