Equations of Circles

Equation of a Circle

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Finding (h,k) and r

Multiple Choice

What is the standard equation of a circle?

• (x-k)² + (y-h)² = r²

• (x+h)² + (y+k)² = r²

• (x-h)² + (y-k)² = r²

• (k-x)² + (h-y)² = r²

Multiple Choice

What does (h,k) standard for in the standard circle equation?

• (h,k) is the center of the circle

• (h,k) is a point on the circle.

• (h,k) is a point that we guess and find

• (h,k) is the distance of the circle

Multiple Choice

What does "h" stand for in (h,k)?

• h is the radius of the circle

• h is the distance of the circle

• h is the y in the coordinate point

• h is the x in the coordinate point

Multiple Choice

What does the "k" in (h,k) stand for?

• k is the y coordinate point in the center of the circle

• k is the x coodinate point in the center of the circle

• k is the radius of the circle

• k is the distance of the circle

Multiple Choice

What does the r in the standard equation stand for?

• r is the distance of the circle

• r is the radius of the circle

• r is the x coordinate of the center of the circle

• r is the y coordinate of the center of the circle

Multiple Choice

Find the center: $$\left(x+4\right)^2+\left(y-2\right)^2\ =\ 25$$

• (4, 2)

• (-4, -2)

• (-4, 2)

• (4, -2)

Multiple Choice

Find the radius: $$\left(x+4\right)^2+\left(y-2\right)^2\ =\ 25$$  

• 2.5

• 5

• 25

• 50

Multiple Choice

Find the center: $$\left(x-7\right)^2+y^2\ =\ 25$$  

• (7, 0)

• (-7, 0)

• (7, 1)

• (-7, -1)

Multiple Choice

Find the diameter: $$\left(x-3\right)^2+\left(y+1\right)^2=49$$  

• 3.5

• 7

• 14

• 49

Multiple Choice

$$x^2+\left(y+10\right)^2=42.25$$  Find the center:

• (0, 10)

• (0, -10)

• (1, 10)

• (1, -10)

Writing the Equation

Multiple Choice

What is the equation of the circle?

center: (5, 3), radius: 2

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

• $$\left(x-5\right)^2+\left(y-3\right)^2=4$$

• $$\left(x+5\right)^2+\left(y+3\right)^2=2$$

• $$\left(x+5\right)^2+\left(y+3\right)^2=4$$

Multiple Choice

What is the equation of the circle?

center: (0, -3), radius: 5

• $$x^2+\left(y+3\right)^2=2.5$$

• $$x^2+\left(y-3\right)^2=5$$

• $$x^2+\left(y+3\right)^2=25$$

• $$x^2+\left(y-3\right)^2=25$$

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 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 Choice

What is the equation of the circle?

• $$\left(x-4\right)^2+\left(y+2\right)^2=3$$

• $$\left(x+4\right)^2+\left(y-2\right)^2=3$$

• $$\left(x-4\right)^2+\left(y+2\right)^2=9$$

• $$\left(x+4\right)^2+\left(y-2\right)^2=9$$

Multiple Choice

Select the graph of the circle: $$\left(x-3\right)^2+y^2=4$$  

Multiple Choice

Select the graph of the circle: $$\left(x-1\right)^2+\left(y+2\right)^2=25$$  

Multiple Choice

Which graph corresponds to

(x-4)²+ (y+4)²=25

• A

• B

• C

• D

Multiple Choice

Which graph corresponds to

(x+2)²+ (y-3)²=36

• A

• B

• C

• D