Question

Could you help me out with a question

Answer 1

The correct is the red circle C

`\text{The center of the circle is (4,-4)}`
`(x-a)^2+(y-b)^2=r^2\ldots.equation\text{ of a circle}`
`\begin{gathered} (x-4)^2+(y+4)^2=25 \\ \text{Comparing the terms in both equations, we have} \\ (x-a)^2=(x-4)^2 \\ x-a=x-4 \\ -a=-4 \\ a=4 \end{gathered}`

Similarly,

`\begin{gathered} (y-b)^2=(y+4)^2 \\ y-b=y+4 \\ -b=4 \\ b=-4 \end{gathered}`

Also,

`\begin{gathered} r^2=25 \\ r=\sqrt[]{25}=_{}\pm5\text{ units} \end{gathered}`

Hence, the correct answer is the red circle (option C)