Rewriting Equations of Circles

Let's put together the two things we learned yesterday!
You'll need paper :)

Rewriting Equations of Circles

This one is already in standard form, so we can immediately see the center and radius.

If it is not in standard form, we need to complete the square to get those "perfect factors"
(it can't be (x-2)(x+3), it must be the same factor twice)

When it's in standard form, it's easy to find the center (h, k) and radius r.

Multiple Choice

$$x^2+\left(y-3\right)^2=9$$   Give the  Center 

• (0,0)

• (0,-3)

• (3,0)

• (0,3)

Multiple Choice

$$x^2+\left(y-3\right)^2=9$$   What is the radius?

• 9

• 6

• 3

• (-3

Multiple Choice

$$\left(x+7\right)^2+\left(y-8\right)^2=25$$   What is the center?

• (-7,8)

• (7,-8)

• (7,8)

• (-7,-8)

Multiple Choice

Write the equation of the circle with center at the origin (0,0) and a diameter of 10

• $$x^2+y^2=10$$  

• $$x^2+y^2=5$$  

• $$x^2+y^2=100$$  

• $$x^2+y^2=25$$  

Multiple Choice

Write the equation of the circle with center at  (-2,4) and a radius of 6

• $$\left(x-2\right)^2+\left(y-4\right)^2=36$$  

• $$\left(x+2\right)^2+\left(y+4\right)^2=36$$  

• $$\left(x+2\right)^2+\left(y-4\right)^2=36$$  

• $$\left(x-2\right)^2+\left(y-4\right)^2=6$$  

Any time you see: x² and x or y² and y, , you have to complete the square.

What if it's not in standard form?

2. Imagine what constant makes it a "perfect trinomial" (ADD to other side to balance!)

1. Put each variable in order

(I don't do this step on the left)
3. Combine all constants on right
4. Write in standard form!

Did you write those steps & example down?

You're going to try now!

I am going to make you a slideshow of me working through each example below. BUT you try them first!!

Multiple Choice

Determine the equation of the circle in standard form:
x² + y² + 4x + 6y - 36 = 0

• (x+2)² + (y+3)² = 49
• (x+2)² + (y+3)² = 13
• (x-2)² + (y-3)² = 49
• (x-2)² + (y-3)² = 13

Multiple Choice

Determine the equation of the circle in standard form: x² + y² + 6x - 12y + 20 = 0

• (x-3)² + (y+6)² = 25
• (x+3)² + (y-6)² = 25
• (x-3)² + (y+6)² = 45
• (x+3)² + (y-6)² = 5

Multiple Choice

Determine the equation of a circle with center (5,-3) and radius of 9

• x²+y²-10x+6y-47=4
• x²+y²-10x-6y-47=0
• 2x²+y²+10x+6y-47=0
• x²+y²-10x+6y-47=0

Multiple Choice

Write the equation of the circle in general form.

• A

• B

• C

• D

Multiple Choice

Convert the equation of the circle from standard to general.

• A

• B

• C

• D

Multiple Choice

Determine the center and radius:
x² + y² - 10x + 8y -8 = 0

• C = (5,-4) r = 7
• C = (-5,4) r = 7
• C = (-4,5) r = 49
• C = (5,-4) r = 49

Multiple Choice

Determine the center and radius: x² + y² + 14x - 2y = -1

• center= (-7,2) radius= 3
• center= (-7,1) radius= 7
• center= (-4,1) radius= 5