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.

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).

The equation of the curve in which the portion of the tangent included between the coordinate axes is bisected at the point of contact, is

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

The equation straight line such that the portion of it intercepted between the coordinate axes is bisected at the point (h,k) 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 line passes through (-3,4) and the portion of the line intercepted between the coordinate axes is bisected at the point then equation of line is (A) 4x-3y+24=0 (B) x-y-7=0 (C) 3x-4y+25=0 (D) 3x-4y+24=0

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

A straight line passes through the point (3, 2) and the portion of this line, intercepted between the positive axes, is bisected at this point. Find the equation of the line.

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