G.12 Equations of Circles

Finding (h,k) and r

From the Equation

• Make the signs on h and k OPPOSITE to get the center

• Take the SQUARE ROOT of r² to get the radius

• If you don't SEE a h or k, then that means the coordinate is ZERO.

To Write the Equation

• Make the signs on the center OPPOSITE before you plug them in for h and k.

• SQUARE the radius (multiply it by itself) before you plug it in for r²

• If you were given the diameter, then divide that by 2 to get the radius. And then square it before you plug it in as r²

From a Graph

• Find the coordinates of the center. Make the signs on both of them OPPOSITE before you plug them in for h and k.

• Find the radius by counting the distance from the center out to the edge of the circle. Then SQUARE that before you plug it in for r²

• 
  

Circle

• A collection of all points (x, y) that are equidistant from a fixed point (h, k)

• Radius ( r ) - the distance between the center and all points (x, y) on the circle

• Center: (h, k)

Standard From of a Circle

Multiple Choice

What is the formula for the standard form equation of a circle?

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

• $$x^2+y^2+Dx+Ey+F=0$$  

• $$x^2-y^2+Dx+Ey+F=0$$  

Multiple Choice

What is the center of the circle with the given equation:

$$\left(x+5\right)^2+\left(y-3\right)^2=9$$ ? 

• $$\left(5,\ 3\right)$$  

• $$\left(5,\ -3\right)$$  

• $$\left(-5,\ 3\right)$$  

• $$\left(-5,\ -3\right)$$  

Multiple Choice

What is the radius of the circle with the given equation: $$\left(x-1\right)^2+\left(y+2\right)^2=25$$ ?

• $$5$$  

• $$25$$  

• $$10$$  

• $$\sqrt[]{5}$$  

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

• (-3, -4)

• (4, 3)

• (-4, -3)

• (3, 4)

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

Which graph corresponds to

(x+2)²+ (y-3)²=36

• A

• B

• C

• D

Multiple Choice

See Picture

• A

• B

• C

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 equation for this circle?

• (x+1)+(y+1)=9

• x²+y²=9

• x+y=9

Multiple Choice

What is the center of the circle whose endpoints of the diameter are (-4, 1) and (4, 5)

• (0, 0)

• (0, 3)

• (3, 0)

• (4, 5)

Multiple Choice

What is the equation of the circle?

center: (4, 0), diameter: 6

• $$\left(x-4\right)^2+y^2=9$$

• $$\left(x+4\right)^2+y^2=9$$

• $$\left(x-4\right)^2+y^2=36$$

• $$\left(x+4\right)^2+y^2=36$$

Multiple Choice

What is the radius of a circle with equation

(x+7)² + (y-2)² = 144 ?

• 7

• 12

• 13