Respuesta :
Answer:
(x - 2)² + (y - 7)² = 26
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 coordinates of the centre are at the midpoint of the endpoints of the diameter and the radius is the distance from the centre to either of the 2 endpoints
Find the centre using the midpoint formula
centre = [ [tex]\frac{1}{2}[/tex](- 3 + 7), [tex]\frac{1}{2}[/tex](8 + 6)] = (2, 7)
to find the radius use the distance formula
r = √(x₂ - x₁)² + (y₂ - y₁)²
with (x₁, y₁ ) = 2, 7) and (x₂, y₂ ) = (7, 6)
r = [tex]\sqrt{(7-2)^2+(6-7)^2}[/tex] = [tex]\sqrt{25+1}[/tex] = [tex]\sqrt{26}[/tex]
centre (2, 7 ) and r² = ([tex]\sqrt{26}[/tex])² = 26, hence
(x - 2)² + (y - 7)² = 26 ← equation of circle
