[" Q.31A 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 P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is

The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is

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

A tangent to the parabola y^(2)=4ax meets axes at A and B .Then the locus of mid-point of line AB is

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.

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)