What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)?

Question

What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)?

Answer 1

Sam,

 

1) Use distance formula to find the radius, r² = (1-1)² + (-2--4)² = 2² (r=2)

2) Use the basic formula to start with x² + y² = 5²

3) recognize that the center is shifted 2 units to the left and 1 unit up

4) shift left by 2 means x+2 and shift up by 1 means y-1

∴ (x+2)² + (y-1)² = 2²

I hope this helps