SOLUTION: for what k will the line y=x+k be the tangent to the hyperbola x^2-4y^2=48?

SOLUTION: for what k will the line y=x+k be the tangent to the hyperbola x^2-4y^2=48?

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Question 1024077: for what k will the line y=x+k be the tangent to the hyperbola x^2-4y^2=48?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let x = y-k.
==>
==>
For tangency, the value of the discriminant must be 0:
==>
==>
==> after simplifying a little further...
==> , or k = 6, -6.
Thus the lines y = x+6 and y = x - 6 are tangent to the hyperbola.

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