Question

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

Answer 1

Answer:

$(x+4)^2 + y^2 = 5$

Step-by-step explanation:

Circle equation: $(x-h)^2 + (y-k)^2 = r^2$

We need to find h, k , $r^2$ to complete the equation.

(h,k) is center point, in this case is given (-4,0) = (h,k)

h=-4

k=0

Substitute to equation: $(x+4)^2+(y-0)^2=r^2$

Use the initial condition: circle passes through the point (-2,1) = (x,y)

x=-2

y=1

Substitute to equation: $(-2+4)^2 + (1)^2=r^2$

Solve for $r^2$ = 5

Final answer: $(x+4)^2 + y^2 = 5$