[FONT=Arial Black]locus question[/FONT] (1 Viewer)

[Sirius Black]

the points P(2ap,ap^2) and Q(2aq,aq^2) a parabola, x^2=4aY, and p+q=2.
By inspection the locus of M (which is the midpt of PQ) is x=2a
but why does it have a restriction that y>/=a? (I know that the locus of M and the parabola intersect at y=a)

thanx guys

 

[mojako]

why am I getting y>=a ???

and how does M and the parabola intersect at y=2??

 

[Sirius Black]

why am I getting y>=a ???

and how does M and the parabola intersect at y=2??

You are right but can u just explain that why does y>=a for the eqn of locus of M to be valid?

 

[mojako]

M is the midpoint of PQ
x
=1/2(2ap+2aq)=...=2

y
=1/2(ap^2+aq^2)
=1/2a[(p+q)^2-2pq]
=2a-apq
=2a-ap(2-p)

then find dy/dp to find minimum point, which is (1,a) in (p,y) format
so y>=a

By inspection the locus of M (which is the midpt of PQ) is x=2a

Do you mean geometrical inspection?
I needed to do the x=1/2(2ap+2aq)=...=2 thing (algebraic).
If you can see it geometrically please tell me how. Thanks.

 

[Managore]

oh god I hate 2ap + ap^2 shit...