Question

PLZZZZZZZZZZ HELP ME!!!!!!!!!!!



A damaged power plant in Japan is closed off for 12 miles in all directions. Let's say that point P represents the location of the plant in a Cartesian coordinate system. The coordinates of P are (3,5). What is the equation of the circle that surrounds the closed-off region? The equation of a circle in standard form is (x - h)^2 + (y - k)^2 = r^2 where (h, k) is the center of the circle, (x,y) is a point on the circle, and r is the radius.

Answer 1

the plant is at P, which is at 3,5.

now, the plant is right at the center of this closed off region, namely P is the center of the circle, since 12 miles in all directions will make a circle with a radius of 12 units, then,

$\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad center~~(\stackrel{3}{{{ h}}},\stackrel{5}{{{ k}}})\qquad \qquad radius=\stackrel{12}{{{ r}}}\\\\ -------------------------------\\\\ (x-3)^2+(y-5)^2=12^2\implies (x-3)^2+(y-5)^2=144$