Answer:
(x - 7)² + (y + 6)² = 10
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.
Using the midpoint formula
[ [tex]\frac{1}{2}[/tex](8 + 6), [tex]\frac{1}{2}[/tex](- 9 - 3) ] = (7, - 6) ← coordinates of centre
The radius r is the distance from the centre to either of the endpoints.
Using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (7, - 6) and (x₂, y₂ ) = (6, - 3), then
r = [tex]\sqrt{(6-7)^2+(-3+6)^2}[/tex]
= [tex]\sqrt{(-1)^2+3^2}[/tex]
= [tex]\sqrt{1+9}[/tex] = [tex]\sqrt{10}[/tex] ⇒ r² = ([tex]\sqrt{10}[/tex] )² = 10
Thus equation of circle is
(x - 7)² + (y - (- 6))² = 10, that is
(x - 7)² + (y + 6)² = 10
