Parametrics (1 Viewer)

[M@ster P]

P, Q are points (2ap, ap^2) and (2aq, aq^2) on the parabola x^2 = 4ay.

i) Find the gradient of the chord PQ and prove that the equation of PQ is y-1/2(p + q)x + apq = 0

ii) Find the coordinates of the point B where the chord meets the axis of the parabola, and deduce that if OM, ON are the ordinates of P, Q (where O is the vertex), then OB^2 = OM . ON

iii) E, F are the feet of the perpendiculars from P, Q to the directrix. Find the coordinates of G the midpoint of EF, and show that GS has gradient -2/(p+q), where S is the focus. Hence deduce that GS is at right angles to PQ.

Can someone draw a diagram of the parabola + worked solutions please, I did i) but ii) and iii) lost me

 

[ianc]

hi there

here is the working for parts ii and iii

hope this helps

 

[M@ster P]

Thx for your help, the reason why I couldnt do the question because I drew the diagram wrong, thx