Question

Identify the equation of the circle that has its center at (-5, -12) and passes through the origin.A. (x−5)2+(y−12)2=269B. (x+5)2+(y+12)2=269C. (x+5)2+(y+12)2=169D. (x−5)2+(y−12)2=169

Answer 1

If the circle has a center at (-5,-12) and passes through the origin, then the radius is:

$r=\sqrt{(-5-0)^2+(-12+0)^2}=13$

Now, the general formula of a circle is given by:

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

Where the circle is (h,k).

Then, we can replace using the values that we know:

$\begin{gathered} (x-(-5))^2+(y-(-12))^2=13^2 \\ (x+5)+(y+12)^2=169 \end{gathered}$

Hence, the correct answer is option C