If $p$ is the length of the perpendicular drawn from the origin to the line $\frac{x}{a}+\frac{y}{b}=1$, then which one of the following is correct?

• Correct answer
  A

  $\frac{1}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}$
• B

  $\frac{1}{p^2}=\frac{1}{a^2}-\frac{1}{b^2}$
• C

  $\frac{1}{p}=\frac{1}{a}+\frac{1}{b}$
• D

  $\frac{1}{p}=\frac{1}{a}-\frac{1}{b}$

Hence, the correct answer is option: 'A'.