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Prove that the segment of tangent to xy...

Prove that the segment of tangent to ` xy=c^(2)` intercepted between the axes is bisected at the point at contact .

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The curve that passes through the point (2, 3) and has the property that the segment of any tangent to it lying between the coordinate axes is bisected by the point of contact, is given by

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The curve that passes through the point (2,3) and has the property that the segment of any tangent to it lying between the coordinate axes is bisected by the point of contact,is given by