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Sagot :
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 ) = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (6, - 7)
(x , y ) = ( [tex]\frac{-2+6}{2}[/tex] , [tex]\frac{1-7}{2}[/tex] ) = ( [tex]\frac{4}{2}[/tex] , [tex]\frac{-6}{2}[/tex] ) = (2, - 3)
The radius is the distance from the centre to either of the endpoints
Calculate the radius using the distance formula
r = [tex]\sqrt{(x_{2}-x_{1})^2+( y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, - 3) and (x₂, y₂ ) = (- 2, 1)
r = [tex]\sqrt{(-2-2)^2+(1-(-3))^2}[/tex]
= [tex]\sqrt{(-4)^2+(1+3)^2[/tex]
= [tex]\sqrt{16+4^2}[/tex]
= [tex]\sqrt{16+16}[/tex]
= [tex]\sqrt{32}[/tex]
Then equation of circle is
(x - 2)² + (y - (- 3) )² = ([tex]\sqrt{32}[/tex] )² , that is
(x - 2)² + (y + 3)² = 32
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