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What are the full range of values for k when the line y equals x -3 meets the curve of x squared -3y squared equals k showing work?
Wiki User
∙ 10y ago
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Emanuel Stehr
Wiki User
∙ 10y agoIf: y = x-3 and x2-3y2 = k
Then: x2-3(x-3)2 = k => -2x2+18x-27-k = 0
Using the discriminant of b2-4ac equals 0: 324-4*-2*(-27-k) = 0 gives k a value of 13.5
So when k = 13.5 there is only one point of contact
And when k > 13.5 there are no points of contact
But when k < 13.5 there are two points of contact
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