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Math·Advanced Math·Nonlinear equations in one variable and systems of equations in two variables

hard

The equation $2x^2-x\sqrt{k}+2y^2+y\sqrt{t}-18=0$, where $k$ and $t$ are positive constants, defines a circle in the $xy$-plane. The radius of this circle is $\sqrt{57}$. Which expression represents the value of $t$?

A

156 - k

B

k - 624

C

624 - k

D

768 - k