Answer:
(x - 2)² + (y + 3)² = 32
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 of the circle is at the midpoint of the diameter
Calculate the centre (x, y ) using the midpoint formula
(x, y ) = ( ,
)
with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (6, - 7)
(x , y ) = ( ,
) = (
,
) = (2, - 3)
The radius is the distance from the centre to either of the endpoints
Calculate the radius using the distance formula
r =
with (x₁, y₁ ) = (2, - 3) and (x₂, y₂ ) = (- 2, 1)
r =
=
=
=
=
Then equation of circle is
(x - 2)² + (y - (- 3) )² = ( )² , that is
(x - 2)² + (y + 3)² = 32