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Need some help with a co-ordinate systems question

I'm having trouble with the following question:

For any rectangular hyperbola C with the equation xy=c2xy=c^2, for c a positive constant, use algebra to determine whether or not the line with equation y=2cxy=2c-x intersects C.

I've tried treating it as a simultaneous equation, but i just end up with c2=2cxx2c^2 = 2cx-x^2.

Any help would be greatly appreciated.
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Original post by finleysmithuk
I'm having trouble with the following question:

For any rectangular hyperbola C with the equation xy=c2xy=c^2, for c a positive constant, use algebra to determine whether or not the line with equation y=2cxy=2c-x intersects C.

I've tried treating it as a simultaneous equation, but i just end up with c2=2cxx2c^2 = 2cx-x^2.

Any help would be greatly appreciated.


What you have done so far is correct. You now have a quadratic in x that you can use to find the x-coordinates of any points of intersection. You don't actually have to find such coordinates, but how can you use the quadratic to find out if there even are any such coordinates?

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