2.04 - Equations of Circles

Equations of Circles

G²

Centered at the origin, we can draw a right triangle inside of a circle and use the coordinates x & y to write the pytahgorean theorem to solve for r (radius)

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Can we move the circle off of the origin?

​Circles on the Coordinate Plane

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Equation for a circle centered at the origin​

We're not in function Kansas anymore

Multiple Choice

Write the standard equation of the circle with the given center and radius; center (0,0) and radius: 3

• x²+y²=3

• x²+y²=6

• x²+y²=9

Multiple Choice

What is the equation of the circle?

• $$\left(x+1\right)^2+\left(y+1\right)^2=4$$

• $$x^2+y^2=4$$

• $$\left(x+4\right)^2+\left(y+4\right)^2=16$$

• $$x^2+y^2=16$$

Multiple Select

Select all the equations for a circle with a diameter of 12.

• $$\left(x+8\right)^2+\left(y-4\right)^2=36$$

• $$\left(x-2\right)^2+\left(y+14\right)^2=144$$

• $$x^2+y^2=36$$

• $$x^2+y^2=144$$

• $$\left(x+6\right)^2+\left(y+6\right)^2=24$$

Equation for any circle

• r is the radius

• h is the x coordinate of the center

• k is the y coordinate of the center​

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​Essentially, you are shifting left/right/up/down relative to a circle centered at the origin

What do you think happens if there was a number outside of the set of parenthesis?

Multiple Choice

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

• (3,2)

• (-3, -2)

• (-2, -3)

• (2, 3)

Multiple Choice

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

• 4

• 2

• 3

• 16

Multiple Choice

In the equation (x-4)²+(x-3)²=25, the center of the circle is at...

• (-3, -4)

• (4, 3)

• (-4, -3)

• (3, 4)

Multiple Choice

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

• (x - 2)² + (y + 5)² = 36

• (x - 5)² + (y + 2)² = 6

• (x + 5)² + (y - 2)² = 36

• (x + 2)² + (y - 5)² = 6

Multiple Choice

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

• A

• B

• C

• D

Draw

Graph the circle: $$9=\left(x-2\right)^2+\left(y+4\right)^2$$