Answer:
(x - 3)² + (y - 2)² = 8
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
The radius is the distance from the centre to a point on the circle
To find r use the distance formula
r = √(x₂ - x₁)² + (y₂ - y₁)²
with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (5, 4)
r = [tex]\sqrt{(5-3)^2+(4-2)^2}[/tex] = [tex]\sqrt{4+4}[/tex] = [tex]\sqrt{8}[/tex]
(x - 3)² + (y - 2)² = ([tex]\sqrt{8}[/tex])²
(x - 3)² + (y - 2)² = 8 ← equation of circle
