if the angle between the lines kx + y + 9 = 0, y - 3x = 4 is 45° the value of k is
1)-1/2
2) 1/3
3) 1/2
4)-1/3
with solutions
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value of k = -1/2 if the angle between the lines kx + y + 9 = 0, y - 3x = 4 is 45°
Step-by-step explanation:
kx + y + 9 = 0
=> y = -kx - 9
slope = - k
y - 3x = 4
=> y = 3x + 4
=> slope = 3
Angle between two lines = 45°
Tan 45 = | (-k - 3)/(1 + (-k)(3)|
=> 1 = = | (-(3 + k)/(1 - 3k) |
=> 1 = | (k + 3)/(3k - 1) |
(k + 3)/(3k - 1) = 1
=> k + 3 = 3k - 1
=> 2k = 4
=> k =2
(k + 3)/(3k - 1) = -1
=> k + 3 = -3k + 1
=> 4k = -2
=> k = -2/4
=> k = -1/2
From the given option value of k = -1/2
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