Question

iDentify the equation of the circle that has its center at (-27, 120) and passes through the origin A. (x−27)^2+(y+120)^2=123 B. (x+27)^2+(y−120)^2=123 C. (x−27)^2+(y+120)^2=15129 D. (x+27)^2+(y−120)^2=15129

Answer 1

The equation of a circle with radius r centered at (h,k) is given by:

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

If the circle passes through the origin, then we have:

$r^2=h^2+k^2$

Then, for a circle centered at (-27,120) passing through the origin, we have:

$\begin{gathered} r^2=(-27)^2+120^2 \\ r^2=15129 \\ (x+27)^2+(y-120)^2=15129 \end{gathered}$

Answer: D