Identify the equation of the circle that has its center at (-16,30) and passes through the origin

(x+16) ² + (y-30) ²=1156

Step-by-step explanation:

We have given:

center at (-16,30). It means h = - 16 and k=30

and it passes through the origin (0,0)

Thus the radius will be distance between (-16,30) and (0,0)

r=√ (-16 - 0) ² + (30-0) ²

r=√256+900

r² = (√1156) ²

r²=1156

Now apply standard equation of circle:

(x-h) ² + (y-k) ² = r²

(x+16) ² + (y-30) ²=1156

Thus the equation is (x+16) ² + (y-30) ²=1156 ...