Question

Determine the equation of a circle with a center at (-4, 0) What is the equation of a circle with a center at (-4, 0)

that passes through the point (-2, 1)?
that passes through the point (-2, 1) by following the
steps below.
© x² + (y + 4)² = √5
1. Use the distance formula to determine the radius:
d=√√(x₂-x₂)²+(₂-V₁)².
2. Substitute the known values into the standard form:
(x-h)²+(y-k)² = r²
O(x-1)² + (y + 2)² = 5
(x+4)² + y² = 5
O(x + 2)² + (y − 1)² = √5

Answer 1

The equation of a circle with a center at (-4, 0) is (x+4)² + y² = r².

To find the equation of a circle with a center at (-4, 0) that passes through the point (-2, 1):

1. Use the distance formula to determine the radius:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
d = √((-2 - (-4))² + (1 - 0)²)
d = √5

2. Substitute the known values into the standard form:
(x - h)² + (y - k)² = r²
(x + 4)² + y² = (√5)²
(x + 4)² + y² = 5

Therefore, the equation of a circle with a center at (-4, 0) that passes through the point (-2, 1) is (x + 4)² + y² = 5.