Help with homework! (1 Viewer)

[Miss-Indecisive]

Need some help with these tangent questions! I have attached them.

Any help or explanations would be greatly appreciated!!


Thanks

 

[anomalousdecay]

 

[Miss-Indecisive]

After working on the question for a bit, I got that answer too I'm just struggling finding the coordinates of K!!!! And the other questions are pretty difficult :S I haven't been able to get them.

 

[Sy123]

b)

Assuming u, v, w are functions of x.











ii) Simply let u = x^5, v = (x-1)^4, w=(x-2)^3

Then substitute it in the above equation.

c)



We can simply differentiate and find the point where there is a horizontal tangent, which happens to be r/(s+r)

However we can simply notice that f is a polynomial with roots 0 and 1. Depending whether r and s are even or odd, they will either be roots where the polynomial goes through them or a turning point exists on them.
Simply draw out the different cases for f and make note that there must exist some point x within 0 and 1 that a horizontal tangent exists. This is the proof.

Or you can just differentiate etc etc.

d)

So its clear that for the previous question that they expect differentiation.

So we know that

The distance from (p,0) to (0,0) is r/(s+r)
And the distance from (p,0) to (1,0) is 1-r/(s+r) = s/(s+r)

If we divide the distances then we arrive at r/s that means the distances are in ratio r : s, that means p divides interval r : s

dii)

 

[Miss-Indecisive]

Thanks for that!!
Do you have any idea how I could find the coordinates of K (first link)? :

 

[anomalousdecay]

We now have 2 equations (Because the coordinates have similar structure)


and

Equate the two equations (1) and (2).





Substituting x into one of the equations gives us:





Therefore:



I didn't look at the other questions though . I am assuming they are all similar and are just year 12 ext1 conics questions.

Rep for Sy123. He did his question right.