Which equation represents a circle that contains the point -5,-3 and has a center at -2,1

(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 =

  =

  =

  = = 5

Thus

(x -(- 2))² + (y - 1)² = 5², that is

(x + 2)² + (y - 1)² = 25 ← equation of circle

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