A circle of constant radius a passes through the origin 0 and cuts the axes of coordinates at points P and Q. Then the equation of the locus of the foot of perpendicular from O to PQ is

• A

  $\left({\mathrm{x}}^2+{\mathrm{y}}^2\right)\left(\frac{1}{{\mathrm{x}}^2}+\frac{1}{{\mathrm{y}}^2}\right)=4{\mathrm{a}}^2$

• B

  ${\left({\mathrm{x}}^2+{\mathrm{y}}^2\right)}^2\left(\frac{1}{{\mathrm{x}}^2}+\frac{1}{{\mathrm{y}}^2}\right)={\mathrm{a}}^2$

• C

  ${\left({\mathrm{x}}^2+{\mathrm{y}}^2\right)}^2\left(\frac{1}{{\mathrm{x}}^2}+\frac{1}{{\mathrm{y}}^2}\right)=4{\mathrm{a}}^2$

• D

  $\left({\mathrm{x}}^2+{\mathrm{y}}^2\right)\left(\frac{1}{{\mathrm{x}}^2}+\frac{1}{{\mathrm{y}}^2}\right)={\mathrm{a}}^2$