The point of intersection of tangents drawn to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` at the points where it is intersected by the line `l x+m y+n=0` , is `((-a^2l)/n ,(b^2m)/n)` (b) `((-a^2l)/m ,(b^2n)/m)` `((a^2l)/m ,(-b^2n)/m)` (d) `((a^2l)/m ,(b^2n)/m)`

Options

A. `((a^(2)l)/(n),-(b^(2)m)/(n))`
B. `(-(a^(2)l)/(n),(b^(2)m)/(n))`
C. `((a^(2)l)/(n),(b^(2)m)/(n))`
D. `(-(a^(2)l)/(n),(-b^(2)m)/(n))`

Explanation

To solve the problem, we need to find the point of intersection of the tangents drawn to the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) at the points where it intersects the line \(lx + my + n = 0\).

### Step-by-step Solution:

1. **Identify the Chord of Contact**:
The chord of contact of tangents from a point \((x_1, y_1)\) to the hyperbola is given by the equation:
\[
\frac{xx_1}{a^2} - \frac{yy_1}{b^2} = 1
...