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Math·Geometry and Trigonometry·Circles

hard

$$x^2+x\sqrt{t}+y^2-y-45=0$$
The given equation, where $t$ is a constant, defines a circle in the $xy$-plane. The radius of this circle is $\sqrt{62}$. What is the value of $t$?

A

33

B

35

C

67

D

69