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Which of the following circles have their centers in the third quadrant? Check all that apply. A.(x + 14)² + (y - 14)² = 84 B.(x + 9)² + (y + 12)² = 36 C.(x + 3)² + (y - 6)² = 44 D.(x + 16)² + (y + 3)² = 17

User BobbyScon
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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

User Dawsy
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