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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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Consider arbitary point of contact . `(ct, (c)/(t))`
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For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

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In the curve x^a y^b=K^(a+b) , prove that the potion of the tangent intercepted between the coordinate axes is divided at its points of contact into segments which are in a constant ratio. (All the constants being positive).

In the curve x^a y^b=K^(a+b) , prove that the potion of the tangent intercepted between the coordinate axes is divided at its points of contact into segments which are in a constant ratio. (All the constants being positive).

In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact. Consider a hyperbola whose center is at the origin. A line x+y=2 touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = 6sqrt2 units. The equation of the tangent to the hyperbola at (-1, 7//2) is

In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact. Consider a hyperbola whose center is at the origin. A line x+y=2 touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = 6sqrt2 units. The equation of the pair of asymptotes is

Show that the tangent at any point of a hyperbola cuts off a triangle of constant area from the asymptotes and that the portion of it intercepted between the asymptotes is bisected at the point of contact.

A conic passes through the point (2, 4) and is such that the segment of any of its tangents at any point contained between the co-ordinate axes is bisected at the point of tangency. Then the foci of the conic are:

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