CIRCLES IN THE COORDINATE PLANE Lesson Slides: 9 Slides

9 Slides • 4 Questions

1

Circle in the Coordinate Plane

2

3

Circle with Center (0,0) and radius (r)

Standard Form
$x^2\ +\ y^2\ =\ r^2$
Ex: $center\ \left(0,0\right)\ and\ radius\ =\ 5\ units$
Standard form: $x^2+y^2=\ 5^2\ \ or\ x^2+y^2=25$
$General\ Form:\ x^2+y^2-25=0$

4

What is the center?

What is the radius?

C (0,0)
r= 3
Standard Form:
$x^2+y^2=9$
General Form: $x^2+y^2-9=0$

5

What is the center?

What is the radius?

C( 0,0)
r=5
Standard Form:
$x^2+y^2=25$
General Form: $x^2-y^2-25=0$

6

Multiple Choice

Find the standard form of a circle if the center is at ( 0,0) and radius of 12 units.

1

$x^2+y^2=\ 12$

2

$x^2+y^2=144$

3

$x^2-y^2=\ 144$

7

Multiple Choice

What is the general form of a circle whose center is at (0,0) and radius of 3 units

1

$x^2+y^2=9$

2

$x^2+y^2=3$

3

$x^2+y^2-9=0$

8

Multiple Choice

What is the radius of the circle whose standard form is

x^2+y^2=\ 36

1

6

2

$\sqrt{6}$

3

36

9

Multiple Choice

What is the radius of the circle if the standard form is

x^2+y^2=\ 2

1

$\sqrt{2}$

2

3

$4$

10

Circle with center at (h,k) and radius (r)

Standard form:

\left(x\ -\ h\right)\ ^2\ +\ \left(y-k\right)^2=\ r^2

General form:

Ax^2+By^2+Cx\ +Dy\ +\ E=\ 0

11

12

What is the center? What is the radius?

C( 1, -2)
r= 2 units
Standard Form:
$\left(x-1\right)^2+\ \left(y+2\right)^2=\ 4$

13

Ex: Center (1,-2) radius= 2

units

Standard Form:
$\left(x\ -1\right)^2\ +\ \left(y+2\right)^2=\ 4$
General form: $\left(\ x^2\ -2x\ +\ 1\right)\ +\ \left(\ y^2\ +\ 4y+\ 4\right)=\ 4$ Combining and Arranging the terms:
$x^2\ +\ y^2\ -\ 2x\ +\ 4y\ +1\ =\ 0$

Circle in the Coordinate Plane

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