The locus of the point of intersection of the tangents drawn at the extremities of a normal chord of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is

• A

  $\frac{a^2}{x^2}-\frac{b^2}{y^2}=a^2+b^2$
• B

  $\frac{a^4}{x^2}-\frac{b^4}{y^2}=\left(a^2-b^2\right)^2$
• C

  $\frac{a^3}{x^2}-\frac{b^3}{y^2}=\left(a^2+b^2\right)^2$
• Correct answer
  D

  $\frac{a^6}{x^2}-\frac{b^6}{y^2}=\left(a^2+b^2\right)^2$

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