Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
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
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
