Answer:
(x - 3)² + (y + 5)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
Here (h, k) = (3, - 5 ) , then
(x - 3)² + (y - (- 5) )² = r² , that is
(x - 3)² + (y + 5)² = r²
r is the distance from the centre to a point on the line
Calculate r using the distance formula
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (3, - 5) and (x₂, y₂ ) = (6, - 4)
r = [tex]\sqrt{(6-3)^2+(-4+5)^2}[/tex]
= [tex]\sqrt{3^2+1^2}[/tex]
= [tex]\sqrt{9+1}[/tex]
= [tex]\sqrt{10}[/tex] ⇒ r² = ([tex]\sqrt{10}[/tex] )² = 10
(x - 3)² + (y + 5)² = 10 ← equation of circle
