Question

Determine the equation of the circle graphed below.

Answer 1

(x - 5)² + (y - 5)² = 18

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 =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

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

r =
`√((8-5)^2+(8-5)^2)`

=
`√(3^2+3^2)`

=
`√(9+9)`

=
`√(18)` ⇒ r² = (
`√(18)` )² = 18

Then

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