A tangent to the hyperbola `x^2/4-y^2/2=1` meets x-axis at `P` and y-axies `Q` LinesPR and QR are drawn such that `OPRQ` is a rectangle (where O is the origin). Then R lies on:

A tangent to the hyperbola x^(2)-2y^(2)=4 meets x-axis at P and y-aixs at Q. Lines PR and QR are drawn such that OPRQ is a rectangle (where O is origin).Find the locus of R.

The tangent at an extremity (in the first quadrant) of latus rectum of the hyperbola (x^(2))/(4)-(y^(2))/(5)=1 meets x -axis and y -axis at A and B respectively.Then (OA)^(2)-(OB)^(2) where O is the origin,equals:

If a tangent to the parabola y^(2)=4ax meets the x -axis at T and intersects the tangents at vertex A at P, and rectangle TAPQ is completed,then find the locus of point Q.

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