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What are the possible values of k in the line y equals 2x plus k that makes contact with the circle x2 plus y2 equals 4?
Wiki User
∙ 6y ago
If: y = 2x+k then y^2 = 4x^2 +4kx +k^2
If: x^2 +y^2 = 4 then 5x^2 +4kx +(k^2 -4) = 0
Using the discriminant: (4k)^2 -4*5*(k^2 -4) = 0
Removing brackets: 16k^2 -20k^2 +80 = 0
Collecting like terms and subtracting 80 from both sides: -4k^2 = -80
Dividing both sides by -4: k^2 = 20
Square root both sides: k = - square root of 20 and k = + square root of 20
Therefore possible values of k are - square root of 20 and + square root of 20
Wiki User
∙ 6y ago
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