Answer:
C
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) = (- 3, 2), thus
(x + 3)² + (y - 2)² = r²
The radius is the distance from the centre of the circle to a point on the circle.
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (6, 4)
r = [tex]\sqrt{(6+3)^2+(4-2)^2}[/tex]
= [tex]\sqrt{9^2+2^2}[/tex] = [tex]\sqrt{85}[/tex]
Hence
(x + 3)² + (y - 2)² = ([tex]\sqrt{85}[/tex] )², that is
(x + 3)² + (y - 2)² = 85 → C
