Answer :
Answer:
(x + 2)² + (y - 1)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.
The radius is the distance from the centre to a point on the circle.
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = ((- 2, 1) and (x₂, y₂ ) = (- 5, - 3)
r = [tex]\sqrt{(-5+2)^2+(-3-1)^2}[/tex]
= [tex]\sqrt{(-3)^2+(-4)^2}[/tex]
= [tex]\sqrt{9+16}[/tex]
= [tex]\sqrt{25}[/tex] = 5
Thus
(x -(- 2))² + (y - 1)² = 5², that is
(x + 2)² + (y - 1)² = 25 ← equation of circle
