IF the tangent at a point on the curve `x^(2//3)+y^(2//3)=a^(2//3)` intersects the coordinate axes in A and B then show that the length AB is a constant.

If the tangent at any point of the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) meets the coordinate axes in A and B, then show that the locus of mid-points of AB is a circle.

Tangent at any point of the curve (x/a)^(2//3)+(y/b)^(2//3)=1 makes intercepts x_1 and y_1 on the axes. Then

The portion of the tangent drawn at any point on x^(2//3)+y^(2//3)=a^(2//3)(agt0) , except the points points on the coordinate axes, included between the the coordinates axes is

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 a triangle made by a tangent at any point on the curve xy =c^(2) and the coordinates axes is of constant area.

Let P be any point on the curve x^(2//3)+y^(2//3)=a^(2//3). Then the length of the segment of the tangent between the coordinate axes in of length