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`

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.

Consider an ellipse (x^2)/4+y^2=alpha(alpha is parameter >0) and a parabola y^2=8x . If a common tangent to the ellipse and the parabola meets the coordinate axes at Aa n dB , respectively, then find the locus of the midpoint of A Bdot

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.

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

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.

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

From the variable point A on circle x^2+y^2=2a^2, two tangents are drawn to the circle x^2+y^2=a^2 which meet the curve at B and Cdot Find the locus of the circumcenter of A B Cdot

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.

A curve C has the property that if the tangent drawn at any point P on C meets the co-ordinate axis at A and B , then P is the mid-point of A Bdot The curve passes through the point (1,1). Determine the equation of the curve.

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.