Prove that the locus of the middle-points of the chords of the hyperbola which pass…

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Prove that the locus of the middle-points of the chords of the hyperbola x2a2−y2b2=1\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 which pass through a fixed point (α,β)(\alpha, \beta) is a hyperbola whose centre is (α2,β2)\left(\frac{\alpha}{2}, \frac{\beta}{2}\right) .

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