Parametrics (PRELIM) (1 Viewer)

[carpe_diem]

The point P(2ap, ap^2) lies on the parabola x^2 = 4ay.

I found that the equation of the tangent was y-px+ap^2=0.

b) Find the point R where this tangent meets the directrix.

Do I need to find the point of intersection? :S

Please show your working out.

Thank you

 

[kr73114]

The point P(2ap, ap^2) lies on the parabola x^2 = 4ay.

I found that the equation of the tangent was y-px+ap^2=0.

b) Find the point R where this tangent meets the directrix.

Do I need to find the point of intersection? :S

Please show your working out.

Thank you

yes you do need to find the point of intersection...form a simultaneous equation
y= px-ap^2 ....(1)
y= -a ....(2)
px-ap^2=-a
px=ap^2-a
x= (ap^2-a)/p
R{(ap^2-a)/p, -a}