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C3 Sample Paper Old Edexcel Textbook Question watch

1. Hi, I am really stuck on this. Please can someone show me how to do it!

f(x) = a/x
g(x) = ax + k

The line y = g(x) is a tangent to the curve y = |f(x)| at the point P, and cuts the curve y = |f(x)| at the point Q.

(b) Show that k = 2a.

Thank you!!
2. (Original post by 1a2b3c4d)
Hi, I am really stuck on this. Please can someone show me how to do it!

f(x) = a/x
g(x) = ax + k

The line y = g(x) is a tangent to the curve y = |f(x)| at the point P, and cuts the curve y = |f(x)| at the point Q.

(b) Show that k = 2a.

Thank you!!
Can you show us the full question, please?
3. (Original post by Zacken)
Can you show us the full question, please?
That is the full question. Part (a) asks you to sketch the curve 'with equation y = |f(x)|.
4. (Original post by Zacken)
Can you show us the full question, please?
5. (Original post by 1a2b3c4d)
That is the full question. Part (a) asks you to sketch the curve 'with equation y = |f(x)|.
*shrugs*

Now consider the two equations:

or

For |f(x)| and g(x) to be tangent, one of these has to have a zero discriminant.
6. Sorry could you take it one step further, I still can't quite get it..
7. (Original post by 1a2b3c4d)
Sorry could you take it one step further, I still can't quite get it..
What is the discriminant of those two quadratic equations?
8. (Original post by 1a2b3c4d)
Hi, I am really stuck on this. Please can someone show me how to do it!

f(x) = a/x
g(x) = ax + k

The line y = g(x) is a tangent to the curve y = |f(x)| at the point P, and cuts the curve y = |f(x)| at the point Q.

(b) Show that k = 2a.

Thank you!!
Following on from Zacken's post, the discriminants are:
(1) k^2-4a(-a) = k^2+4a^2, and (2) k^2-4a(a)=k^2-4a^2.
So in case 1, k^2=-4a^2, which is impossible as the LHS is positive and the RHS is negative.
Thus we go to case 2: k^2=4a^2 -> k=+/-2a, and since k and a are positive, k=2a, as required.

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