Question

write an equation for the following circle in standard form based on the information given: center (-4,1) radius:3 please show steps to get it done

Answer 1

We are asked to write the equation for the circle in standard form based on the information below.

center = (-4, 1)

radius = 3

Recall that the equation of the circle in standard form is given by

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

Where (h, k) are the coordinates of the center and r is the radius.

Substituting the coordinates of the center and value of the radius we get

`\begin{gathered} (x-(-4))^2+(y-1)^2=(3)^2 \\ (x+4)^2+(y-1)^2=9 \end{gathered}`

Therefore, the equation of the given circle is

`(x+4)^2+(y-1)^2=9`