Let $L=\lim _{x \rightarrow 0} \frac{a-\sqrt{a^2-x^2}-\frac{x^2}{4}}{x^4}$, $a>0$. If $L$ is finite, then

• Correct answer
  A

  $a=2$
• B

  $a=1$
• Correct answer
  C

  $L=\frac{1}{64}$
• D

  $L=\frac{1}{32}$

Hence, the correct answer is options: 'A', 'C'.