Circle Equations

Equation of a Circle

Learning Target: Write the equation of a circle and graph a circle from it's equation.

​Dr. Tom Giles

Equation of a Circle

Learning Target: Write the equation of a circle and graph a circle from it's equation.

​With center of circle at origin of coordinate plane, Circle Equation is:

(x - h)² + (y - k)² = r²

x² + y² = 25

Multiple Choice

What does the equation of a circle with center at (0,0) look like?

• $$y=x^2$$

• $$y=mx+b$$

• $$x^2+y^2=r^2$$

• $$y=a\left(x-h\right)^2+k$$

Equation of a circle with center at (0,0)

Multiple Choice

What is the equation for this circle?

• (x+1)+(y+1)=9
• x²+y²=9
• x+y=9

Multiple Choice

Write the equation at the origin with radius 6.  

• x^2 + y^2 = 6
• x^2 + y^2 = 36
• x  + y = 6
• x + y = 36

Multiple Choice

What is the center of the circle with equation x² + y² = 1?

• (1, 1)
• (0, 0)
• not enough information
• (-1, -1)

What if the center isn't (0,0)?

We use the point (h,k) to talk about the center of the circle..

Equation of a circle

Open Ended

Why has there not been an h and k value in the equations we have looked at so far, like this one?

$$x^2+y^2=81$$  

Writing Equations of Circles

We can write equations of circles from their graphs.

Locate the center of the circle. This usually marked with a dot

Multiple Choice

What is the center of this circle?

• (2, 2)

• (2, -2)

• (0, 0)

• (-2, 2)

Writing Equations of Circles

The other piece of information we need is the radius.

You can calculate the radius by counting the number of units from the center to any point on the circle.

Multiple Choice

What is the radius of this circle?

• 2

• 6

• 3

• 5

Writing Equations of Circles

Multiple Choice

What is the equation of the circle?

• (x+1)^2 +(y +1)^2 = 3

• (x+1)^2 + (y -1)^2 = 3

• (x+1)^2 +(y +1)^2 = 9

• (x-1)^2 + (y -1)^2 = 9

Multiple Choice

What is the center and radius for a circle with the equation:
(x-4)²+(y+2)²=25

• C:(4, -2), r=5
• C:(-4, 2), r=5
• C:(4, -2), r=25
• C:(-4, 2), r=25

Multiple Choice

What is the radius of the circle
(x+7)²+(y-2)²=144?

• 7
• 12
• 13

Multiple Choice

Write the equation of a circle with center (7, 0) with radius 3. 

• (x - ^7)^2 + y^2 = 9
• x^2 + (y -7)^2 = 9
• (x - 7)^2 + y^2 = 3
• x^2 + (y -7)^2 = 3

Multiple Choice

Which graph corresponds to 
(x)²+ (y-6)²=9

• A
• B
• C
• D