Question 1056918: Find the values of k if the line x+y=k is a tangent to the circle x^2+y^2=8
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi there,
x + y = k
Rearrange
y = k - x
Substitute y = k - x
into:
x^2 + y^2 = 8
x^2 + (k - x)^2 = 8
x^2 + k^2 - 2kx + x^2 = 8
Collect like terms
x^2 + x^2 - 2kx + k^2 - 8 = 0
2x^2 - 2kx + k^2 - 8 = 0
Using the discriminant b^2 - 4ac
(-2k)^2 - 4(2)(k^2 - 8) = 0
4k^2 - 8k^2 + 64 = 0
-4k^2 + 64 = 0
-4k^2 = -64
Divide both sides by -4
k^2 = 16
k = √16
k = 4 and -4
Hope this helps :-)
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