If the roots of the equation

$\left({\mathrm{x}}_1^2-{\mathrm{a}}^2\right){\mathrm{m}}^2-2{\mathrm{x}}_1{\mathrm{y}}_1\mathrm{m}+{\mathrm{y}}_1^2+{\mathrm{b}}^2=0\left(\mathrm{a}>\mathrm{b}\right)$

are the slopes of two perpendicular lines intersecting at $\mathrm{P}\left({\mathrm{x}}_1,{\mathrm{y}}_1\right),$ then the locus of P is 

• A

  ${\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{a}}^2+{\mathrm{b}}^2$

• B

  ${\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{a}}^2-{\mathrm{b}}^2$

• C

  ${\mathrm{x}}^2-{\mathrm{y}}^2={\mathrm{a}}^2+{\mathrm{b}}^2$

• D

  ${\mathrm{x}}^2-{\mathrm{y}}^2={\mathrm{a}}^2-{\mathrm{b}}^2$