There exist two points `P` and `Q` on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` such that `PObotOQ`, where `O` is the origin, then the number of points in the `xy`-plane from where pair of perpendicular tangents can be drawn to the hyperbola , is

Options

A. `0`
B. `1`
C. `2`
D. infinite

Explanation

To solve the problem, we need to find the number of points in the \(xy\)-plane from which a pair of perpendicular tangents can be drawn to the hyperbola given by the equation:

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

### Step-by-Step Solution:

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