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# Help H/W in for tomorrow :S watch

1. Line Y = 3X + 1
Curve X^2 + Y^2 = K

FIND VALUES OF K FOR WHICH THE LINE IS A TANGENT TO THE CURVE?

IM DOING WJEC SO PLEASE USE A METHOD WHICH IS RELEVANT

This is how I tried it:

As Y (line) = Y (curve) therefore
(3X + 1)^2 = K - X^2
I used the fact that Y = Y

So we get

(3X +1)(3X+1)= 9X^2 + 3X + 3X +1
9X^2 + 3X + 3X +1 = K - X^2
8X ^2 + 6X + 1 - K = 0

So now we can use the discriminant on it, as its in ax^2 + bx + c = 0 form.

a = 8
b = 6

B^2 - 4AC
(6)^2 - 4(8)(K+1) = 0
36 - 32(K+1) = 0
36 - 32K - 32 = 0
4 = 32K
4/32 = K
1/8 = K

2. You've got the right method, but you made an error here:
(Original post by Tempa)
9X^2 + 3X + 3X +1 = K - X^2
8X ^2 + 6X + 1 - K = 0
3. 9X^2 + 3X + 3X +1 = K - X^2

This ^ is correct but the line after it is wrong. Can you correct it?
4. as far as i know 9x^2 - x^2 is 8x^2?
5. sh!!!t
6. (Original post by Tempa)
as far as i know 9x^2 - x^2 is 8x^2?
But the -x² is on the other side of the equation, so you have to add it.

Silly mistake.
7. 9X^2 + 3X + 3X +1 = K - X^2
10 ^2 + 6X + 1 - K = 0

So now we can use the discriminant on it, as its in ax^2 + bx + c = 0 form.

a = 10
b = 6

B^2 - 4AC
(6)^2 - 4(10)(K+1) = 0
36 - 40(K+1) = 0
36 - 40k - 40 = 0
-4 - 40k = 0
40k= -4
k = -0.1 or -1/10

is this correct?
8. (Original post by Get me off the £\?%!^@ computer)
nah not sarcasm mate just i make silly mistakes like that all the time its annoying
9. (Original post by Tempa)
9X^2 + 3X + 3X +1 = K - X^2
10 ^2 + 6X + 1 - K = 0

So now we can use the discriminant on it, as its in ax^2 + bx + c = 0 form.

a = 10
b = 6

B^2 - 4AC
(6)^2 - 4(10)(K+1) = 0
36 - 40(K+1) = 0
36 - 40k - 40 = 0
-4 - 40k = 0
40k= -4
k = -0.1 or -1/10

is this correct?
Nope, your 1-k magically became k+1 somehow (it should be 1-k).
10. ah sh1t another one of my silly mistakes fml
11. 9X^2 + 3X + 3X +1 = K - X^2
10 ^2 + 6X + 1 - K = 0

So now we can use the discriminant on it, as its in ax^2 + bx + c = 0 form.

a = 10
b = 6

B^2 - 4AC
(6)^2 - 4(10)(K-1) = 0
36 - 40(K-1) = 0
36 - 40k + 40 = 0
76 - 40k = 0
76 = 40k
k = 76/40
12. 9X^2 + 3X + 3X +1 = K - X^2
10 ^2 + 6X + 1 - K = 0

So now we can use the discriminant on it, as its in ax^2 + bx + c = 0 form.

a = 10
b = 6

B^2 - 4AC
(6)^2 - 4(10)(K-1) = 0
36 - 40(K-1) = 0
36 - 40k + 40 = 0
76 - 40k = 0
76 = 40k
k = 76/40
13. accident, but im i correct?
14. (Original post by Tempa)
accident, but im i correct?
Nope, your 1-k magically became k-1. It should still be 1-k.
15. so is k = 1/10
16. (Original post by nuodai)
Nope, your 1-k magically became k-1. It should still be 1-k.
1/10?
17. (Original post by Tempa)
1/10?
Got there eventually! Well done.
18. (Original post by nuodai)
Got there eventually! Well done.
any tips to improve my maths i need a A* in alev

had a flukey a* at gcse
19. (Original post by Tempa)
any tips to improve my maths i need a A* in alev

had a flukey a* at gcse
Just do as many practice questions as you can really. Also try checking your answers for yourself without asking other people -- it'll help you get better at spotting common and silly mistakes (like the ones you were making here). Like here you could have put into the second equation, substituted the first equation into the second equation and used the discriminant to make sure there is only one root. [That's what I did to check your answer.]
20. (Original post by Tempa)
any tips to improve my maths i need a A* in alev

had a flukey a* at gcse
I got by 2ums at GCSE, and 1ums at a2. Soloman past papers all the way.

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Updated: October 3, 2010
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