Use the equation below to identify the value fo each variable for the circle.

standard form equation of a circle

(h, v) = center
r = radius

h=
v =
r =

then, write the standard form equation of the circle.

The equation of the circle in standard form is: (x - 2)² + (y - 4)² = 9

Step-by-step explanation:

* Lets revise the standard form of the equation of the circle

- If the center of the circle is point (h , v) and the radius of the

 circle is r, then the standard form of the equation of the circle

 is (x - h)² + (y - v)² = r²

- (x , y) a general point on the circle

* Lets look to the picture

- The center of the circle is point (2 , 4)

- The highest point on the circle is (2 , 7) and the lowest point

 on the circle is (2 , 1)

∴ The diameter of the circle = 7 - 1 = 6

∵ The radius = 1/2 the diameter

∴ The radius of the circle = 1/2 × 6 = 3

* Now we can write the equation of the circle

∵ h = 2 and v = 4

∵ r = 3

∴ (x - 2)² + (y - 4)² = 3²

∴ The equation of the circle in standard form is:

   (x - 2)² + (y - 4)² = 9

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