(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) = [ [tex]\frac{1}{2}[/tex] (3 - 7), [tex]\frac{1}{2}[/tex] (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
