Answer:
(x - 1)² + (y - 2)² = 20
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
Given the endpoints, then the centre is at the midpoint
C = [ [tex]\frac{-3+5}{2}[/tex], [tex]\frac{0+4}{2}[/tex] ] = (1, 2 )
The radius is the distance from the centre to either of the 2 endpoints.
Use the distance formula to find r
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ )= (- 3, 0)
r = [tex]\sqrt{(-3-1)^2+(0-2)^2}[/tex]
= [tex]\sqrt{(-4)^2+(-2)^2}[/tex]
= [tex]\sqrt{16+4}[/tex]
= [tex]\sqrt{20}[/tex]
Thus equation of circle is
(x - 1)² + (y - 2)² = ([tex]\sqrt{20}[/tex] )² , that is
(x - 1)² + (y - 2)² = 20
