If the product of the lengths of the perpendicular drawn from the ends of a diameter of the circle $x^2+y^2=4$ on to the line $x+y+1=0$ is maximum, then the two ends of that diameter are

• A

  $(-2,0),(2,0)$
• B

  $(\sqrt{3}, 1),(-\sqrt{3},-1)$
• Correct answer
  C

  $(\sqrt{2}, \sqrt{2}),(-\sqrt{2},-\sqrt{2})$
• D

  $(0,2),(0,-2)$

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