Maths 2u and ext 1 Thread (1 Viewer)

[Boxxxhead]

I've been cruising this year so far, I'm coming 3/22 in 3-unit, but all of a sudden I have NO idea about the parametric representations of the parabola. I can't work out stuff like this:

P(4t , 2t²) and Q(8t , 8t²) are two variable points on the parabola x² = 8y. Tangents from P and Q intersect at T. Find the cartesion equation of the locus of T.

I really need help with this topic :S

 

[pLuvia]

I've been cruising this year so far, I'm coming 3/22 in 3-unit, but all of a sudden I have NO idea about the parametric representations of the parabola. I can't work out stuff like this:

P(4t , 2t²) and Q(8t , 8t²) are two variable points on the parabola x² = 8y. Tangents from P and Q intersect at T. Find the cartesion equation of the locus of T.

I really need help with this topic :S

lol.. havent learnt that yet... we're only doin trig rite now..

 

[Emma-Jayde]

At my school we did things in an almost random order. We jumped around a bit because there are 3u topics that you can't do unless you've done a certain 2u topic, that's why.
Some school do the whole 2u course in preliminary and the whole 3u course in year 12.

 

[pLuvia]

are the 4u classes usually in the morning?? bcoz that will be a real bitch lol coz usually morning classes start at 7.30am .... and i will have a jap ext class in the morning as well..~~ ..

 

[klaw]

Expand and equate co-efficients:
2x^2 + x + 1 = ax^2 - ax - 2 + bx - b + c
So a = 2
1 = b - a
so b = 3
c - b - 2 = 1
so c = 6

c = 8 I think... not 6

When x=0, a=2, b=3, c=8
LHS: 0+0+1 = 1
RHS: 2(1)(-2)+3(-1)+8 = -4-3+8 = 1 = RHS

You expanded the thingy wrong, it should expand to ax^2+(a-2a+b)x+(c-2a-b)

 

[Templar]

P(4t , 2t²) and Q(8t , 8t²) are two variable points on the parabola x² = 8y. Tangents from P and Q intersect at T. Find the cartesion equation of the locus of T.

8y=x^2
y'=x/4

Tangent at P
y-2t^2=t(x-4t)
y=tx-2t^2

Tangent at Q
y-8t^2=2t(x-8t)
y=2tx-8t^2

They intersect, so
2tx-8t^2=tx-2t^2
tx=6t^2
x=6t
y=4t^2

x^2=36t^2
=9y

Cartesian equation is 9y=x^2

 

[klaw]

I've been cruising this year so far, I'm coming 3/22 in 3-unit, but all of a sudden I have NO idea about the parametric representations of the parabola. I can't work out stuff like this:

P(4t , 2t²) and Q(8t , 8t²) are two variable points on the parabola x² = 8y. Tangents from P and Q intersect at T. Find the cartesion equation of the locus of T.

I really need help with this topic :S

You sure that's the co-ordinate of Q? I thought that points on the parabola follow (2at, at^2)?

 

[Templar]

That's for 4ay=x^2. Sub in coordinates of Q into 8y=x^2 and it works.

 

[klaw]

edit:wrong answer (writing maths on comp is so hard, and your efforts are so wasted when you find out it's wrong )