Write the standard form of the equation of the circle which the given characteristics endpoints of a diameter (11, -3), (3, 13)

(x - 7)² + (y - 5)² = 78

Step-by-step explanation:

The standard form of the equation of a circle 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

Calculate the centre using the midpoint formula

midpoint = [0.5(x₁ + x₂), 0.5(y₁ + y₂) ]

with (x₁, y₁ ) = (11, - 3) and (x₂, y₂ ) = (3, 13)

centre = [0.5(11 + 3), 0.5(- 3 + 13) ] = (7, 5)

The radius is the distance from the centre to either of the endpoints

Calculate the radius using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (7, 5) and (x₂, y₂ ) = (3, 13)

r =

  =

  = =

Hence

(x - 7)² + (y - 5)² = ()², that is

(x - 7)² + (y - 5)² = 78 ← equation of circle

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step-by-step explanation: