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How do you find the value of k when the line y equals x - 3 touches the curve x squared - 3y squared equals k?
Wiki User
∙ 13y ago
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Loyal Mayert
Wiki User
∙ 13y agoEquation 1: y = x-3 => y2 = 3y2-18x+27 when both sides are squared and multiplied by 3
Equation 2: x2-3y2 = k => x2-k = 3y2 => 3y2 = x2 -k
By definition:
3x2-18x+27 = x2-k => 2x2-18x+27+k = 0
Use the discriminant b2-4ac = 0 to find the value of k:
b2-4ac = 0 => 182-4*2*(27+k) = 0
108-8k = 0
-8k = -108
k = 13.5
Check: 182-4*2*(27+13.5) = 0
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