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Math·Geometry and Trigonometry·Circles

hard

A circle in the $xy$-plane has its center at $(-5,-6)$ and intersects the line $y=a$ at exactly one point, where $a$ is a positive constant. Which equation defines this circle?

A

$(x-5{)}^2+(y-6{)}^2=(a-6{)}^2$

B

$(x-5{)}^2+(y-6{)}^2=(a+6{)}^2$

C

$(x+5{)}^2+(y+6{)}^2=(a-6{)}^2$

D

$(x+5{)}^2+(y+6{)}^2=(a+6{)}^2$