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If the normal at a pont P to the hyperbo...

If the normal at a pont `P` to the hyperbola `x^2/a^2 - y^2/b^2 =1` meets the x-axis at `G`, show that the `SG = eSP.S` being the focus of the hyperbola.

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To solve the problem, we need to show that the distance \( SG \) from the focus \( S \) of the hyperbola to the point \( G \) where the normal at point \( P \) intersects the x-axis is equal to \( e \times SP \), where \( SP \) is the distance from the focus \( S \) to the point \( P \) on the hyperbola. ### Step-by-Step Solution: 1. **Identify the Hyperbola and Points**: The equation of the hyperbola is given by: \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 ...
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