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What are the two possible values of k when the line y equals x plus k is a tangent to the circle x2 plus y2 equals 25?
Wiki User
∙ 6y ago
Tangent line equation: y = x+k
Circle equation: x^2 +y^2 = 25
If: y = x+k then y^2 = (x+k)^2 => y^2 = x^2 +2kx+k^2
So: x^2 +x^2 +2kx +k^2 = 25
Transposing terms and collecting like terms: 2x^2 +2kx +(k^2 -25) = 0
Using the discriminant: 4k^2 -4*2*(k^2 -25) = 0
Which is the same as: 4k^2 -8k^2 +200 = 0
Collecting like terms and subtracting 200 from both sides: -4k^2 = -200
Divide both sides by -4: k^2 = 50
Square root both sides: k = + or - the square root of 50
Therefore it follows that the possible values of k are plus or minus the square root of 50
Wiki User
∙ 6y ago
Wiki User
∙ 6y agok = -5*sqrt(2) and 5*sqrt(2).
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What are the possible values of k when the line y equals kx -2 is a tangent to the circle y equals x2 -8x plus 7?
If: y = kx -2 is a tangent to the curve (which is not a circle) of y = x^2 -8x +7 Then: kx -2 = x^2 -8x +7 Transposing and collecting like terms: (8x+kx) -x^2 -9 = 0 Using the discriminant: (8+k)^2 -4*-1*-9 = 0 Multiplying out the brackets and collecting like terms: 16k +k^2 +28 = 0 Factorizing the above: (k+2)(k+14) = 0 meaning k = -2 or k = -14 Therefore the possible values of k are -2 or -14
What are the possible values of k in the line y equals kx -2 which is tangent to the curve y equals x squared -8x plus 7?
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When a series of events takes place each with a fixed number of possible values the of the number of values of each event equals the total number of possible outcomes?
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What are the possible values of k when the line y equals kx -2 is a tangent to the circle y equals x2 -8x plus 7?
If: y = kx -2 is a tangent to the curve (which is not a circle) of y = x^2 -8x +7 Then: kx -2 = x^2 -8x +7 Transposing and collecting like terms: (8x+kx) -x^2 -9 = 0 Using the discriminant: (8+k)^2 -4*-1*-9 = 0 Multiplying out the brackets and collecting like terms: 16k +k^2 +28 = 0 Factorizing the above: (k+2)(k+14) = 0 meaning k = -2 or k = -14 Therefore the possible values of k are -2 or -14
What are the possible values of k in the line y equals kx -2 which is tangent to the curve y equals x squared -8x plus 7?
The possible values for k are -2 and -14 because in order for the line to be tangent to the curve the discriminant must be equal to 0 as follows:- -2x-2 = x2-8x+7 => 6-x2-9 = 0 -14x-2 = x2-8x+7 => -6-x2-9 = 0 Discriminant: 62-4*-1*-9 = 0
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