If (x)/(a)+(y)/(b)=2 touches the curve (...

If `(x)/(a)+(y)/(b)=2` touches the curve `(x^(n))/(a^(n))+(y^(n))/(b^(n))=2` at the point `(alpha, beta)`, then

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Prove that the locus of the middle-points of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which pass through a fixed point (alpha, beta) is a hyperbola whose centre is ((alpha)/(2), (beta)/(2)) .

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MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE

If (x)/(a)+(y)/(b)=2 touches the curve (x^(n))/(a^(n))+(y^(n))/(b^(n))...
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