Find the equation of a circle given only its diameter endpoints: (-2,1) and (6,-7)

(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

m

step-by-step explanation: