Question

What is the center and radius of the circle with equation (x + 4)2 + (y - 1)2 = 16?

Answer 1

The equation of a circle, given center (h, k) with radius r is given by the formula

`(x-h)^2+(y-k)^2=r^2`

Comparing, this equation with the given equation

`(x+4)^2+(y-1)^2=16`

we have the foolowing:

x-h = x + 4

subtract x from both sides

-h = 4

h= -4

y-k = y-1

subtract y from both sides

-k = -1

k = 1

`\begin{gathered} r^2=16 \\ r=\sqrt[]{16} \\ r=4 \end{gathered}`

The center of the circle is ( -4, 1) while the radius is 4 units