Question

8.(09.04 LC)A circle is centered at (-4, -6) and has a radius of 3. Which of the following is the equation for this circle? (6 points)neva agilO (x + 4)2 + (y + 6)2 = 30 (x – 4)2 + (y – 5)2 = 9O (x – 4)2 + (y - 6)2 = 3O (x + 4)2 + (y + 6)2 = 9

Answer 1

The general standard equation for the circle centered at (h, k) with radius r is given to be:

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

From the question provided, we have the center to be (-4, -6) and a radius of 3. Therefore, we have:

`\begin{gathered} (h,k)=(-4,-6) \\ r=3 \end{gathered}`

Hence, the equation of the circle is given to be:

`\begin{gathered} (x-\lbrack-4\rbrack)^2-(y-\lbrack-6\rbrack)^2=3^2 \\ \Rightarrow(x+4)^2-(y+6)^2=9 \end{gathered}`

The correct option is the LAST OPTION.