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FP1 translation of curve help

hello i am currently stuck on a bunch of questions where i am told to find what the value of k where a curve has been translated by a vector which i have to find. An example here

The curve with equation x2 - 2x - y2 + 4y = 20 has been translated onto the curve with equation x2 -8x - y2 -2y = k . Find the value of k and find the value of k and the vector of the translation.

Well i can find the vector by completing the square on both equation , coming out to be [ 3 ]
[-3]
However im not sure about how to find k, could anyone give me a detailed run through please. Thanks in advance.
Original post by League_Masters
hello i am currently stuck on a bunch of questions where i am told to find what the value of k where a curve has been translated by a vector which i have to find. An example here

The curve with equation x2 - 2x - y2 + 4y = 20 has been translated onto the curve with equation x2 -8x - y2 -2y = k . Find the value of k and find the value of k and the vector of the translation.

Well i can find the vector by completing the square on both equation , coming out to be [ 3 ]
[-3]
However im not sure about how to find k, could anyone give me a detailed run through please. Thanks in advance.


Expand (x3)22(x3)(y+3)2+4(y+3)=20(x-3)^2-2(x-3)-(y+3)^2+4(y+3)=20 ?
Original post by Mr M
Expand (x3)22(x3)(y+3)2+4(y+3)=20(x-3)^2-2(x-3)-(y+3)^2+4(y+3)=20 ?



Uh im not too sure where you got that equation from.
Original post by League_Masters
Uh im not too sure where you got that equation from.


I have just translated the hyperbola.

You know if you have a circle x2+y2=r2x^2+y^2=r^2 and you move the centre from (0, 0) to (a, b) it becomes (xa)2+(yb)2=r2(x-a)^2+(y-b)^2=r^2 ? This is the same thing.
Original post by Mr M
I have just translated the hyperbola.

You know if you have a circle x2+y2=r2x^2+y^2=r^2 and you move the centre from (0, 0) to (a, b) it becomes (xa)2+(yb)2=r2(x-a)^2+(y-b)^2=r^2 ? This is the same thing.



So with the first equation, the original:
x22x=(x1)21[br](y24y)=(y2)2+4[br](x1)2(y2)2=15 x^2 - 2x = (x-1)^2 - 1[br] - (y^2 - 4y) = -(y-2)^2 + 4[br](x-1)^2 - (y-2)^2 = 15

The second equation in that format was [br][br](x4)2(y+1)2=k15[br][br](x-4)^2 - (y+1)^2 = k-15
So then the curve has been translated through vector, 3 units to the right, 3 units down so [3, -3]. But im unsure what k is.
(edited 9 years ago)
Original post by League_Masters
So with the first equation, the original:
x22x=(x1)21[br](y24y)=(y2)2+4[br](x1)2(y2)2=15 x^2 - 2x = (x-1)^2 - 1[br] - (y^2 - 4y) = -(y-2)^2 + 4[br](x-1)^2 - (y-2)^2 = 15

So then the curve has been translated through vector, 3 units to the right, 3 units down so [3, -3]. But im unsure what k is.



I mean i checked the answer that i got which was correct, but my answer to k is incorrect...
Original post by League_Masters
I mean i checked the answer that i got which was correct, but my answer to k is incorrect...


Look at the very first equation you have in your opening post? The one I gave was a translation of this. Expand my version and you have k.
Original post by Mr M
Look at the very first equation you have in your opening post? The one I gave was a translation of this. Expand my version and you have k.


yeah, woops, found k which was 2, overcomplicated it :smile:. Thank you
Original post by League_Masters
(x1)2(y2)2=17(x-1)^2 - (y-2)^2 = 17

Fixed that for you.
(edited 9 years ago)
Original post by Mr M
Fixed that for you.



yeah that was my mistake, woopsies
Original post by League_Masters
...

Original post by Mr M
....

Is this for edexcel? I thought the only graph stuff on FP1 was parametric equations.
Original post by MathMeister
Is this for edexcel? I thought the only graph stuff on FP1 was parametric equations.


No idea. Core 1 knowledge is probably sufficient anyway.
Original post by Mr M
No idea. Core 1 knowledge is probably sufficient anyway.

Do you teach A level?
Original post by MathMeister
Do you teach A level?


Yes.
Original post by MathMeister
Is this for edexcel? I thought the only graph stuff on FP1 was parametric equations.



This stuff is on the AQA spec.

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