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If normal at P to a hyperbola of eccentr...

If normal at P to a hyperbola of eccentricity e intersects its transverse and conjugate axes at L and M, respectively, then prove that the locus of midpoint of LM is a hyperbola. Find the eccentricity of this hyperbola

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To solve the problem step-by-step, we will follow the given instructions and derive the necessary equations. ### Step 1: Define the Hyperbola The equation of the hyperbola with transverse axis along the x-axis and conjugate axis along the y-axis is given by: \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \] where \( e \) (eccentricity) is defined as \( e = \sqrt{1 + \frac{b^2}{a^2}} \). ...
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