Answer:
(x - 8)² + (y - 13)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 centre is located at the midpoint of the endpoints of the diameter.
Use the midpoint formula to find the centre
[[tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] ]
with (x₁, y₁ ) = (5, 9) and (x₂, y₂ ) = (11,17)
centre = ( [tex]\frac{5+11}{2}[/tex], [tex]\frac{9+17}{2}[/tex] ) = (8, 13)
The radius is the distance from the centre to either end of the diameter
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (8, 13) and (x₂, y₂ ) = (5, 9)
r = [tex]\sqrt{(5-8)^2+(9-13)^2}[/tex]
= [tex]\sqrt{(-3)^2+(-4)^2}[/tex]
= [tex]\sqrt{9+16}[/tex] = [tex]\sqrt{25}[/tex] = 5 ⇒ r² = 25
Hence
(x - 8)² + (y - 13)² = 25
