Answer:
(x - 2)² + (y - 4)² = 17
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 centre is at the midpoint of the endpoints of the diameter, that is
x = [tex]\frac{6-2}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2 and y = [tex]\frac{5+3}{2}[/tex] = [tex]\frac{8}{2}[/tex] = 4
centre = (2, 4 )
The radius is the distance from the centre to either of the endpoints
Using the distance formula to find r
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (- 2, 3)
r = [tex]\sqrt{(-2-2)^2+(3-4)^2}[/tex]
= [tex]\sqrt{(-4)^2+(-1)^2}[/tex]
= [tex]\sqrt{16+1}[/tex]
= [tex]\sqrt{17}[/tex] ⇒ r² = 17
Thus the equation of the circle is
(x - 2)² + (y - 4)² = 17
