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What are the range of values of k when y equals 2x plus k and x squared plus y squared equals 4 but do not intersect?
Wiki User
∙ 13y ago
Equation 1: y = 2x+k => y2 = 4x2+4kx+k2 when both sides are squared
Equation 2: x2+y2 = 4 => y2 = 4-x2 when rearranged
So by definition:
4x2+4kx+k2 = 4-x2 => 5x2+4kx+k2-4 = 0
If the values are tangent to the curve then the discriminant b2-4ac = 0
b2-4ac = 0 => 16k2-4*5*(k2-4) = 0
16k2-20k2+80 = 0 => 4k2-5k2+20 = 0
-k2+20 = 0 => -k2 = -20
Therefore the values of k are: plus or minus the square root of 20
Check: (4*k2)-(5*k2)+20 = 0
Wiki User
∙ 13y ago
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