Respuesta :
Answer:
(x - 8)² + (y + 6)² = 25
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
Here (h, k ) = (8, - 6 ) , then
(x - 8)² + (y - (- 6))² = r² , that is
(x - 8)² + (y + 6)² = r²
The radius is the distance from the centre to a point on the circle
Calculate r using the distance formula
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (8, - 6 ) and (x₂, y₂ ) = (5, - 2 )
r = [tex]\sqrt{(5-8)^2+(-2-(-6))^2}[/tex]
= [tex]\sqrt{(-3)^2+(-2+6)^2}[/tex]
= [tex]\sqrt{9+4^2}[/tex]
= [tex]\sqrt{9+16}[/tex]
= [tex]\sqrt{25}[/tex]
= 5
Then equation of circle is
(x - 8)² + (y + 6)² = 5² , that is
(x - 8)² + (y + 6)² = 25
