If a curve passing through `(1,1)` is such that the tangent drawn at any point `P` on it intersects the `x` -axis at `Q` and the reciprocal of abscissa of point `P` is equal to twice the `x` - intercept of tangent at `P`.Then the equation of the curve is
(a) `y^(2)=x`
(b) `x^(2)-2y-1`
(c) `3x^(2)-2y^(2)=1`
(d) `2x^(2)-y^(2)=1`