The curve represented by $\frac{x^2}{12-\alpha}+\frac{y^2}{\alpha-10}=1$ is

• A

  a hyperbola for some values of $\alpha$ in $(10,12)$
• B

  an ellipse for all values of $\alpha$ in $(10,12)$
• Correct answer
  C

  a circle for some value of $\alpha$ in $(10,12)$
• D

  a hyperbola for all values of $\alpha$ in $(10,12)$

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