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

hard

$$\begin{gathered} y=4x^2+47 \\ y=px+43 \end{gathered}$$

In the given system of equations, $p$ is a positive constant. The graphs of the equations in the given system intersect at exactly one point, $(x,y)$, in the xy-plane. What is the value of $p$?

A

1

B

8

C

51

D

90