Statement 1 : If from any point $P\left(x_1,y_1\right)$ on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$ , tangents are drawn to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1,$ then the corresponding chord of contact lies on an other branch of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$ Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.

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