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.

Show that the lenght of the portion of the tangent to the curve x^(2/3)+y^(2/3)=a^(2/3) at any point of it, intercept between the coordinate axes is contant.

Show that the length of the portion of the tangent to the curve x^((2)/(3))+y^((2)/(3))=4 at any point on it, intercepted between the coordinate axis in constant.

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,

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.

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-

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.

A straight line passes through the point (1,2) and is such that the protion of it intercepted between the axes is divided internally at the points in the ratio 3:2 . Find the equation of the line .

If length of tangent at any point on the curve y=f(x) intercepted between the point and the x-axis is of length 1 . Find the equation of the curve.