Find the standard form of the equation of the circle with endpoints of a diameter at the points (3,4) and (-7,6)

(x + 2)² +(y - 5)² = 26

The equation of a circle in standard form is

(x - a)² + (y - b)² = r²

where (a , b) are the coordinates of the centre and r the radius

The centre is at the midpoint of the endpoints of the diameter and r is the distance from the centre to either of the 2 endpoints

Find centre using the ' midpoint formula'

(a , b) = [ (3 - 7), (4 + 6) ] = (-2 , 5)

to find r use the ' distance formula '

with (-2 ,5) and (3 , 4)

r = √(3 + 2)² + (4 - 5)² = √(25 + 1 ) = √26 ⇒ r² = (√26)² = 26

(x + 2)^² + (y - 5)² = 26 → equation in standard form

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step-by-step explanation:

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