Презентация на тему Circles

circle with its center at the origin is
Notice

r is the radius of the circle so if we take the square root of the right hand side, we'll know how big the radius is.

circle is at the origin and the radius is

This is r2 so r = 3

Center at (0, 0)

Count out 3 in all directions since that is the radius

at the origin then the equation for the standard

The center of the circle is at (h, k).

The center of the circle is at (h, k) which is (3,1).

Find the center and radius and graph this circle.

The radius is 4

This is r2 so r = 4

in standard form for example:
You can find the center

Remember center is at (h, k) with (x - h) and (y - k) since the x is plus something and not minus, (x + 2) can be written as (x - (-2))

This is r2 so r = 2

(x - (-2))

But what if it was not in standard form but multiplied out (FOILED)

Moving everything to one side in descending order and combining like terms we'd have:

we'd have to complete the square on both the

Group x terms and a place to complete the square

Group y terms and a place to complete the square

Move constant to the other side

4

4

16

16

Write factored and wahlah! back in standard form.

Complete the square

the circle with center at (0, 0) and radius

Let's sub in center and radius values in the standard form

0

0

7

at (0, 0) that passes through the point (-1,

The point (-1, -4) is on the circle so should work when we plug it in the equation:

Since the center is at (0, 0) we'll have

Subbing this in for r2 we have:

at (-2, 5) and radius 6
Subbing in the values

-2

5

6

at (8, 2) and passes through the point (8,

Subbing in the center values in standard form we have:

8

2

Since it passes through the point (8, 0) we can plug this point in for x and y to find r2.

graph:
To get in standard form we don't want coefficients

So the center is at (0, 0) and the radius is 8/3.

9

9

9

Remember to square root this to get the radius.

graph:
Remember the center values end up being the opposite

So the center is at (-4, 3) and the radius is 5.

the x's and y's to get in standard form.
Group

Group y terms and a place to complete the square

Move constant to the other side

9

9

4

4

Write factored for standard form.

Find the center and radius of the circle:

So the center is at (-3, 2) and the radius is 4.