If we have a look at the equation, we see that the eccentricity of this hyperbola is the square root of 1+9^2/3^2. i.e. eccentricity = 2.
If we then look at the focus of this hyperbola, we see that it is 2(sqrt3), which is also the x-coordinate of P. Therefore we know that since P is the extremity of a focal chord, and it lies on the same vertical line as the focus, then P is the end of the latus rectum.
By recalling the length of a latus rectum of a hyperbola as 2.(b^2/a^2), we clearly see that the length is 6 units.
By subtracting 6 from 2(sqrt3), we then know the x-coordinate of Q for answer.
Most of these conics questions should have an alternative solution if they give you a point on the conic not in parametric form, most of time it's just if you can see it or not
