If the chords of contact of tangents fromtwo points `(x_1,y_1) and (x_2,y_2)` to the hyperbola `x^2/a^2-y^2/b^2=1` are at right angles, then `(x_1x_2)/(y_1y_2)` is equal to (a) `a^2/(-b^2)` (b) `b^2/(-a^2)` (c) `b^4/(-a^4)`

Options

A. `-(a^(2))/(b^(2))`
B. `-(b^(2))/(a^(2))`
C. `-(b^(4))/(a^(4))`
D. `-(a^(4))/(b^(4))`

Explanation

To solve the problem, we need to find the value of \( \frac{x_1 x_2}{y_1 y_2} \) given that the chords of contact from two points \( (x_1, y_1) \) and \( (x_2, y_2) \) to the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) are at right angles.

### Step-by-Step Solution:

1. **Write the equation of the hyperbola:**
The hyperbola is given by:
\[
\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1
...