Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Get immediate and reliable solutions to your questions from a community of experienced professionals on our 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
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
