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FP3 hyperbola question

ImageUploadedByStudent Room1456913338.986178.jpgImageUploadedByStudent Room1456913347.399922.jpg
Hi can someone help me with Q9 a)? I have no idea how to find a and b. Thanks.


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Original post by 123321123
ImageUploadedByStudent Room1456913338.986178.jpgImageUploadedByStudent Room1456913347.399922.jpg
Hi can someone help me with Q9 a)? I have no idea how to find a and b. Thanks.


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ImageUploadedByStudent Room1456913658.223320.jpgImageUploadedByStudent Room1456913665.089966.jpg
Better pics of the question and my work so far. Help needed thanks.


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Original post by 123321123
ImageUploadedByStudent Room1456913658.223320.jpgImageUploadedByStudent Room1456913665.089966.jpg
Better pics of the question and my work so far. Help needed thanks.


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You know that if you plug y = 3x + 10 into the equation of your hyperbola and look at the discriminant of the resulting quadratic, you should know that the discriminant = 0.That gives you one equation in a and b.

Then you know the asymptotes of the hyperbola are given by y=±bxay = \pm \frac{bx}{a} (from the formula booklet) so that give you a second equation in a and b.

Then simultaneous.
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Original post by Zacken
You know that if you plug y = 3x + 10 into the equation of your hyperbola and look at the discriminant of the resulting quadratic, you should know that the discriminant = 0.That gives you one equation in a and b.

Then you know the asymptotes of the hyperbola are given by y=±bxay = \pm \frac{bx}{a} (from the formula booklet) so that give you a second equation in a and b.

Then simultaneous.


Thanks for ur rely
ImageUploadedByStudent Room1456917240.541207.jpg
Hi this is what I ve got after combining two equations. But when I do simultaneous they cancelled out.


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Original post by 123321123
Thanks for ur rely
ImageUploadedByStudent Room1456917240.541207.jpg
Hi this is what I ve got after combining two equations. But when I do simultaneous they cancelled out.


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Could you show me your full working out?
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Original post by Zacken
Could you show me your full working out?


My full working is on the second picture on the top. The two equation I got for a and b can be cancelled out as one of them is the square root of the other. So wondering if there is other method. Thanks.


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Original post by 123321123
My full working is on the second picture on the top. The two equation I got for a and b can be cancelled out as one of them is the square root of the other. So wondering if there is other method. Thanks.


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I don't understand why you're looking at the gradient of the curve. Plug in your tangent and look at the discriminant of the quadratic, equate the discriminant to zero.
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because the tangent equation gives me that the gradient is 3, so I thought if I could differentiate the hyperbola equation and my dy/dx equal to 3. Still confused.


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Original post by Zacken
I don't understand why you're looking at the gradient of the curve. Plug in your tangent and look at the discriminant of the quadratic, equate the discriminant to zero.


because the tangent equation gives me that the gradient is 3, so I thought if I could differentiate the hyperbola equation and my dy/dx equal to 3. Still confused.



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Original post by Zacken
I don't understand why you're looking at the gradient of the curve. Plug in your tangent and look at the discriminant of the quadratic, equate the discriminant to zero.



I tried ur method and got a equation of a and b, but it is the same as what I have got in my full working shown on the top.


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Bit busy, hopefully somebody else will pop in and have a look at this or I'll do it myself later on tonight
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Original post by Zacken
Bit busy, hopefully somebody else will pop in and have a look at this or I'll do it myself later on tonight


I solved it thanks for your help.


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