simple maximisation/minisation question (1 Viewer)

[kooltrainer]

a) Draw the region between the parabola y^2 = 4ax and latus rectum x=a .
b) Hence, find the dimensions of the rectangle with maximum area in this region.

thx =)

 

[ssglain]

Here you go.

 

[SoulSearcher]

Here you go.

I must say your handwriting has kept up amazingly well after all these months after school. Mine's has gone to the shits

 

[kooltrainer]

ehh thx, but i got another problem .. a locus one

Q: p(x,y) lies on the line y=4x+3 . show tht M (midpoint of OP) has co ordinates (x/2 , 1/2(4x+3)) hence , find the locus of M

 

[ssglain]

I must say your handwriting has kept up amazingly well after all these months after school. Mine's has gone to the shits

I swear, this does not resemble my pre-HSC handwriting.

 

[SoulSearcher]

Co-ordinates of O - (0, 0) [Taken this as an assumption, but unless defined otherwise, O is usually taken to be the point of origin on the Cartesian plane]
Co-ordinates of P - (x₁, y₁), y = 4x+3

When x = x₁, y = 4x₁+3, hence y₁ = 4x₁+3

Therefore co-ordinates of M (midpoint of OP) is ([0+x₁]/2, [0+y₁]/2)
= (x₁/2, y₁/2)
= (x₁/2, [4x₁+3]/2)

To find the locus of M, let
x = x₁/2 ... (1)
y = [4x₁+3]/2 ... (2)

Hence, from (1),
2x = x₁ ... (3)

Substitute (3) into (2),
y = [4(2x)+3]/2
y = [8x + 3]/2, locus of M

I swear, this does not resemble my pre-HSC handwriting.

Still better than mine

 

[ssglain]

ehh thx, but i got another problem .. a locus one

Since you go to FSHS, you mustn't live far from Burwood. How about I tutor you?

 

[ssglain]

Co-ordinates of O - (0, 0) [Taken this as an assumption, but unless defined otherwise, O is usually taken to be the point of origin on the Cartesian plane]
Co-ordinates of P - (x₁, y₁), y = 4x+3

When x = x₁, y = 4x₁+3, hence y₁ = 4x₁+3

Therefore co-ordinates of M (midpoint of OP) is ([0+x₁]/2, [0+y₁]/2)
= (x₁/2, y₁/2)
= (x₁/2, [4x₁+3]/2)

To find the locus of M, let
x = x₁/2 ... (1)
y = [4x₁+3]/2 ... (2)

Hence, from (1),
2x = x₁ ... (3)

Substitute (3) into (2),
y = [4(2x)+3]/2
y = [8x + 3]/2, locus of M

Still better than mine

You beat me to it. Haha.

 

[SoulSearcher]

You beat me to it. Haha.

I'm amazed I still know this stuff, I last learnt this around 2 years ago, and probably did this type of question only a couple times last year :uhhuh:

kooltrainer, I definitely recommend that you take on sslgain as a tutor, she is obviously talented at maths and will help you improve in the subject greatly

 

[kooltrainer]

Since you go to FSHS, you mustn't live far from Burwood. How about I tutor you?

i'l think abt it.. thing is, it takes me 45 min to get to FSHS, its gona take me 1 hr to get to burwood

 

[ssglain]

i'l think abt it.. thing is, it takes me 45 min to get to FSHS, its gona take me 1 hr to get to burwood

We can have our session on a school day (once term recommences, of course) - it only takes about 10 mins by train from Petersham to Burwood.