Question
The number of real values of k for which the lines x – 2y + 3 = 0, kx + 3y + 1 = 0 and 4x – ky + 2 = 0 are concurrent is
- 0
- 1
- 2
- infinite
Hint:
We are given equation of three lines. We have to find the value of K such that the given lines are concurrent. It means they pass through single point. For lines to be concurrent, the determinant of their coefficients should be zero. We have to find the real values of K.
.
The correct answer is: 0
The given lines are as follows
x - 2y + 3 = 0
Kx + 3y + 1 = 0
4x - ky + 2 = 0
We will take the determinant of the coefficients
To find the roots we will use the formula to solve quadratic equations.
we will first find the value of b2 - 4ac
b2 - 4ac = (-5)2 - 4(3)(38)
= 25 - 456
= -431
So, b - 4ac < 0
It doesn't have any real values. As, the value under is negative.
The answer is zero.
For such questions, we should know properties of concurrent lines.
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