Question

Give the equation for a circle with the given center and radius.Center at (-10, -4), radius = 5A. (x−10)^2+(y−4)^2=25B. (x−4)^2+(y−10)^2=5C. (x+4)^2+(y+10)^2=5D. (x+10)^2+(y+4)^2=25

Answer 1

$D)(x+10)^2+(y+4)^2=5^2=25$

Explanation

Step 1

We know that the general equation for a circle is

$\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \end{gathered}$

where

(h,k) is the center of the circel

and r is the radius

then, all we need to do is replace

Let

$\begin{gathered} \text{center}\Rightarrow(h,k)\Rightarrow(-10,-4) \\ \text{radius}\Rightarrow r\Rightarrow5 \end{gathered}$

replace the values

$\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (x-(-10))^2+(y-(-4))^2=5^2 \\ (x+10)^2+(y+4)^2=5^2=25 \end{gathered}$

therefore, the answer is

$D)(x+10)^2+(y+4)^2=5^2=25$

I hope this helps you