Question

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

t passes through the point (-2, 1)?
x2 + (y + 4)2 = square root 5
(x - 1)2 + (y + 2)2 = 5
(x + 4)2 + y2 = 5
(x + 2)2 + (y – 1)2 = square root 5

Answer 1

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

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`