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,

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).

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-

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

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.

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+n)=a^(m-n)y^(2n) , prove that the m t h power of the sub-tangent varies as the n t h power of the sub-normal.

Find the locus of the mid-point of the portion of the line x cosalpha+ysinalpha=4 intercepted between the axes of coordinates.

Show that the sum of the intercept on the coordinates axes of tangent to the curve sqrt(x)+sqrt(y)=sqrt(a) at any point on it is constant.

A curve is such that the mid-point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the y-axis lies on the line y=x. If the curve passes through (1,0), then the curve is