Answer:
(x - 3)² + (y + 2)² = 25
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 calculate r use the distance formula
r = √(x₂ - x₁)² + (y₂ - y₁ )²
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, - 2)
r = [tex]\sqrt{(3-0)^2+(-2-2)^2}[/tex] = [tex]\sqrt{9+16}[/tex] = [tex]\sqrt{25}[/tex] = 5
(x - 3)² + (y + 2)² = 25 ← equation of circle
