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).

Find the eqution of the curve in which the portion of the tangent between the coordinate axes is bisected at the point of contact.

Find the equation of the curve whose length of the tangent at any point on ot, intercepted between the coordinate axes is bisected by the point of contact.

In the curve x^(m)y^(n)=k^(m+n)(m,n, k gt0) prove that the portion of the tangent intercepted between the coordinate axes is divided at its point of contact in a constant ratio,

The equation of the curve in which the portion of the tangent between the coordinate axes is bisected at the point of contact is a/an-

Show that the length of the tangent to the curve x^(m)y^(n)=a^(m+n) at any point of it, intercepted between the coordinate axes is divided internally by the point of contact in the ratio m:n.

The sum of the intercepts cut off from the coordinate axes by a variable line is 14 units . Find the locus of the point which divides internally the portion of the line intercepted between the coordinate axes in the ratio 3:4 .

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 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