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.

Find the equation of the tangent to the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) at the point (alpha,beta)

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

A variable straight line through the point of intersection of the two lines (x)/(3)+(y)/(2)=1and(x)/(2)+(y)/(3)=1 meets the coordinate axes at A and B . Find the locus of the middle point of AB.

A variable line through the point of intersection of the lines x/a+y/b=1 and x/b+y/a=1 , meets the co-ordinate axes in A and B, then the locus of mid point of AB is

The equation of the tangent to the curve x^((2)/(3))+y^((2)/(3))= a^((2)/(3)) at the point (a cos^(3) alpha , a sin^(3) alpha) is-

The tangent at any point on the curve x=acos^3theta,y=asin^3theta meets the axes in Pa n dQ . Prove that the locus of the midpoint of P Q is a circle.

Consider the family of circles x^2+y^2=r^2, 2 < r < 5 . If in the first quadrant, the common tangnet to a circle of this family and the ellipse 4x^2 +25y^2=100 meets the co-ordinate axes at A and B, then find the equation of the locus of the mid-point of AB.

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.

A straight line through the point of intersection of the lines x+2y = 4 and 2x +y =4 meets the coordinates axes at A and B. The locus of the midpoint of AB is

The tangent at any point P on the circle x^(2)+y^(2)=2 , cuts the axes at L and M. Find the equation of the locus of the midpoint L.M.