Tangents at any point on the hyperbola `x^2/a^2-y^2/b^2=1` cut the axes at A and B respectively, If the rectangle at OAPB (where O is origin) is completed then locus of point P is given by

If the tangent drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at any point P meets the coordinate axes at the points A and B respectively. If the rectangle OACB (O being the origin) is completed, where C lies on (x^2)/(a^2)-(y^2)/(b^2)=lambda . Then, the value of lambda is:

Let P(theta_1) and Q(theta_2) are the extremities of any focal chord of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 whose eccentricity is e. Let theta be the angle between its asymptotes. Tangents are drawn to the hyperbola at some arbitrary points R. These tangent meet the coordinate axes at the points A and B respectively. The rectangle OABC (O being the origin) is completedm, then Q.Locus of point C is

Let P(theta_1) and Q(theta_2) are the extremities of any focal chord of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 whose eccentricity is e. Let theta be the angle between its asymptotes. Tangents are drawn to the hyperbola at some arbitrary points R. These tangent meet the coordinate axes at the points A and B respectively. The rectangle OABC (O being the origin) is completedm, then Q.Locus of point C is

Tangents at P to rectangular hyperbola xy=2 meets coordinate axes at A and B, then area of triangle OAB (where O is origin) is _____.

The tangent at any point P on the circle x^2 + y^2 = 2 cuts the axes in L and M . Find the locus of the middle point of LM .

The tangent at any point P on the circle x^2 + y^2 = 2 cuts the axes in L and M . Find the locus of the middle point of LM .