Answer:
B and D
Explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
(h, k ) are the coordinates of the centre and r is the radius
circles with centres in the third quadrant will have both x and y coordinates negative , that is (- x, - y )
Consider each equation
A : (x + 14)² + (y - 14)² = 84
has centre (- 14, 14 ) ← in second quadrant
B : (x + 9)² + (y + 12)² = 36
has centre (- 9, - 12 ) ← in third quadrant
C : (x + 3)² + (y - 6)² = 44
has centre (- 3, 6 ) ← in second quadrant
D : (x + 16)² + (y + 3)² = 17
has centre (- 16, - 3 ) ← in third quadrant
the circles with centres in the third quadrant are B and D