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.

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 tangent at an arbitrary point R on the curve (x^(2))/(p^(2))-(y^(2))/(q^(2))=1 meets the line y=(q)/(p)x at the point S, then the locus of mid-point of RS is

Consider the family of circles If in the 1st quadrant, the common tangent to a circle of this family and the ellipse 4x^(2)+25y^(2)=100 meets the co-ordinate axes at A and B, then show that the locus of mid point of AB is 4x^(2) + 25y^(2) = 4x^(2)y^(2)

If the tangent at the point (a,b) on the curve x^(3)+y^(3)=a^(3)+b^(3) meets the curve again at the point (p,q) then show that bp+aq+ab=0

A tangent (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the axes at A and B.Then the locus of mid point of AB is

The tangent at any point on the curve x=a cos^(3)theta,y=a sin^(3)theta meets the axes in P and Q. Prove that the locus of the midpoint of PQ is a circle.

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at A and B . Then find the locus of the midpoint of A Bdot