Question

Determine the equation of a circle with a center at (–4, 0) that passes through the point (–2, 1) by following the steps below.

Use the distance formula to determine the radius: d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
Substitute the known values into the standard form: (x – h)² + (y – k)² = r².
What is the equation of a circle with a center at (–4, 0) that passes through the point (–2, 1)?

x2 + (y + 4)² = StartRoot 5 EndRoot
(x – 1)² + (y + 2)² = 5
(x + 4)² + y² = 5
(x + 2)² + (y – 1)² = StartRoot 5 EndRoot

Answer 1

Center (h,k)=(-4,0). Radius r = distance from (-4,0) to (-2,1) = sqrt[(−2+4)^2 + (1−0)^2] = sqrt(4+1)=sqrt(5), so r^2 = 5.

Equation: (x+4)^2 + y^2 = 5.