The locus of the point of intersection of the tangents at the end-points of normal chords of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`, is

Options

A. `(a^(6))/(x^(2))+(b^(6))/(y^(2))=(a^(2)+b^(2))^(2)`
B. `(a^(6))/(x^(2))-(b^(6))/(y^(2))=(a^(2)+b^(2))^(2)`
C. `(a^(6))/(x^(2))-(b^(6))/(y^(2))=(a^(2)-b^(2))^(2)`
D. `(a^(6))/(x^(2))+(b^(6))/(y^(2))=(a^(2)-b^(2))^(2)`

Explanation

To find the locus of the point of intersection of the tangents at the end-points of normal chords of the hyperbola given by the equation

\[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1, \]

we will follow these steps:

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