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What is the value of k when the curve x squared plus y squared equals k touches the line y equals 3x plus 1 at just one point?
Wiki User
∙ 7y ago
If: x^2 +y^2 = k then y^2 = k-x^2
If: y = 3x +1 then y^2 = (3x +1)^2 => y^2 = 9x^2 +6x +1
So: 9x^2 +6x +1 = k -x^2
Transposing terms: 10x^2 +6x +(1 -k) = 0
Using the discriminant b^2 -4ab = 0: 36 -4*10*(1 -k)= 0 => -k = -1/10
Therefore: k = 1/10
Wiki User
∙ 7y ago
Wiki User
∙ 7y agok = 0.1
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