The equation of a circle whose end points of a diameter are $\left(\mathrm{x}_1, \mathrm{y}_1\right)$ and $\left(\mathrm{x}_2, \mathrm{y}_2\right)$ is

• A

  $\left(x-x_1\right)\left(x-x_2\right)+\left(y-y_1\right)\left(y-y_2\right)=x^2+y^2$
• B

  $\left(x-x_1\right)^2+\left(y-y_1\right)^2=x_2 y_2$
• C

  $x^2+y^2+2 x_1 x_2+2 y_1 y_2=0$
• Correct answer
  D

  $\left(x-x_1\right)\left(x-x_2\right)+\left(y-y_1\right)\left(y-y_2\right)=0$

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