Answer:
2nd option
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.
The coordinates of the centre is the average of the coordinates of the endpoints.
centre = ( [tex]\frac{-4+2}{2}[/tex], [tex]\frac{7-1}{2}[/tex] ) = ([tex]\frac{-2}{2}[/tex] , [tex]\frac{6}{2}[/tex] ) = (- 1, 3 )
the radius is the distance from the centre to either of the endpoints
using the distance formula to calculate r
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2[/tex]
with (x₁, y₁ ) = (- 1, 3 ) and (x₂, y₂ ) = (2, - 1 )
r = [tex]\sqrt{(2-(-1))^2+(-1-3)^2}[/tex]
= [tex]\sqrt{(2+1)^2+(-4)^2}[/tex]
= [tex]\sqrt{3^2+16}[/tex]
= [tex]\sqrt{9+16}[/tex]
= [tex]\sqrt{25}[/tex]
= 5
then equation of circle is
(x - (- 1) )² + (y - 3)² = 5² , that is
(x + 1)² + (y - 3)² = 25