If the tangent at any point P on the curve `x^m y^n = a^(m+n), mn != 0` meets the coordinate axes in A, B then show that `AP:BP` is a constant.

IF the tangent at any point P on the curve x^my^n=a^(m+n) , mn ne 0 meets the coordinate axes in A.B then show that AP:BP is a constant.

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.

The subtangent at any point on the curve x^(m)y^(n)=a^(m+n) varies as

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.