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(FP1 new spec) What do we treat as the general point on the ellipse?

For some questions, we use the trignometric general point on the ellipse, but for some questions ive noticed such as
'P and Q are two distinct points on the ellipse described by the equation x^2 + 4y^2 = 4
The line l passes through the point P and the point Q.
The tangent to the ellipse at P and the tangent to the ellipse at Q intersect at the point (r, s).
Show that an equation of the line l is
4sy + rx = 4'

the general point is taken as (x,y). When do we know which one to choose? Its the only thing im struggling with in conic sections so help on this would make me a whole lot more confident in this topic