# Thread: Parametric Equations

1. ## Parametric Equations

Hey everyone thnx in advance!!

Normal to the parabola x=2at, y=at^2 from points P(2ap,ap^2) and Q(2aq,aq^2) intersect at N. Find the equation of the locus of N if PQ passes through the point (0,3a)

2. ## Re: Parametric Equations

Hey,

1. Find the equation for the parabola with the parameter removed
2. Find the equation of the normal at P or Q then find the other by inspection
3. Find the equation of the line PQ
4. Sub in the given point to find an expression for pq
5. Find the point of int of the normals
6. Find an expression for p+q
7. Remove the parameters in the y co.ord of the point of int of the normals

It seems long so in a test they'll give you some of the components etc.

Also just checking that the answer is $x^{2}=9a(y-5a)$ ?

3. ## Re: Parametric Equations

Originally Posted by BenHowe
Hey,

1. Find the equation for the parabola with the parameter removed
2. Find the equation of the normal at P or Q then find the other by inspection
3. Find the equation of the line PQ
4. Sub in the given point to find an expression for pq
5. Find the point of int of the normals
6. Find an expression for p+q
7. Remove the parameters in the y co.ord of the point of int of the normals

It seems long so in a test they'll give you some of the components etc.

Also just checking that the answer is $x^{2}=9a(y-5a)$ ?
That is indeed the answer.

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