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CONICSChapter 7

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

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!!!!

Example 1

Geometric locus Bisector of the 1st

quadrant Locus Equation yx (x0)

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!!!!

Example 2

Geometric locus Horizontal line through

(0,2) Locus Equation y2

CIRCLES

- Section 7.2

Investigation

radius

Can you find how long the radius is? c2 a2

b2 r2 22 22 r2 8 r v8 r 2.82

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

Circle Centered at the origin

Standard Form Equation x2 y2 r2 M? ? ?

d(0,M) r

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

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)

Circle NOT centered at the origin

Standard Form Equation (x-h)2 (y-k)2 r2 M?

?(w,r) ? d(w,M) r

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

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