The equation of the locus of the foot of the perpendicular drawn from the centre of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ to any tangent of the ellipse is

• Correct answer
  A

  $\left(x^2+y^2\right)^2=a^2 x^2+b^2 y^2$
• B

  $\left(x^2-y^2\right)^2=a^2 x^2+b^2 y^2$
• C

  $\left(x^2+y^2\right)^2=a^2 x^2-b^2 y^2$
• D

  $\left(x^2-y^2\right)^2=a^2 x^2-b^2 y^2$

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