$f(x)$ is a continuous function on $\mathbb{R}$ and $y=f(x)$ is a curve. If $(\alpha, \beta)$ is a point such that $\beta=f(\alpha)$ and $p\alpha+m\beta+n=0$ $(p \neq 0, m \neq 0)$,then which one of the following is true?

• A
  When $p+mf^{\prime}(\alpha)=0$,$px+my+n=0$ is a tangent to the curve $y=f(x)$ at $(\alpha, \beta)$.
• B
  $px+my+n=0$ is always a tangent to the curve $y=f(x)$.
• C
  When $p+mf^{\prime}(\alpha) \neq 0$,$px+my+n=0$ intersects the curve $y=f(x)$ at $(\alpha, \beta)$.
• D
  $px+my+n=0$ is never a tangent to the curve $y=f(x)$.