Determine the equation of the circle graphed below.

(x - 5)² + (y - 5)² = 18

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k ) = (5, 5) , then

(x - 5)² + (y - 5)² = r²

r is the distance from the centre to a point on the circle

Calculate r using the distance formula

r =

with (x₁, y₁ ) = (5, 5) and (x₂, y₂ ) = (8, 8)

r =

  =

   =

   = ⇒ r² = ( )² = 18

Then

(x - 5)² + (y - 5)² = 18 ← equation of circle

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