Answer:
(x - 2)² + (y - 3)² = 29
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.
Use the midpoint formula to find the centre
[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]
with (x₁, y₁ ) = (- 3, 5) and (x₂, y₂ ) = (7, 1), thus
centre = [ 0.5(- 3+7), 0.5(5 + 1) ] = [0.5(4), 0.5(6) ] = (2. 3 )
The radius is the distance from the centre to either of the endpoints of the diameter.
Calculate the radius using the distance formula
√ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (7, 1)
r = [tex]\sqrt{(7-2)^2+(1-3)^2}[/tex]
= [tex]\sqrt{5^2+(-2)^2}[/tex]
= [tex]\sqrt{25+4}[/tex] = [tex]\sqrt{29}[/tex], hence
(x - 2)² + (y - 3)² = ([tex]\sqrt{29}[/tex] )², that is
(x - 2)² + (y - 3)² = 29 ← equation of circle
