If the lines 2x – 3y + k = 0, 3x – 4y – 13 = 0 and 8x – 11y – 33 = 0 are concurrent, then k = ___________.

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Solution

We know, three lines

$a x + b y + c = 0 l x + m y + n = 0 p x + q y + r = 0 are concurrent if |\begin{matrix} a & b & c \\ l & m & n \\ p & q & r \end{matrix}| = 0 for 2 x - 3 y + k = 0, 3 x - 4 y - 13 = 0 and 8 x - 11 y - 33 = 0 i . e . |\begin{matrix} 2 & - 3 & k \\ 3 & - 4 & - 13 \\ 8 & - 11 & - 33 \end{matrix}| = 0 |\begin{matrix} 2 & - 3 & k \\ 3 & - 4 & - 13 \\ 8 & - 11 & - 33 \end{matrix}| = 0 2 (33 \times 4 - 13 \times 11) + 3 (- 99 + 104) + k (- 33 + 32) = 0 2 (132 - 143) + 3 (5) - k = 0 i . e . 2 (- 11) + 15 - k = 0 i . e . - 22 + 15 - k = 0 i . e . - 7 - k = 0 i . e . k = - 7$

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Similar questions

2 x - 3 y + λ = 0

3 x - 4 y - 13 = 0

8 x - 11 y - 33 = 0

| λ |

The value of k so that the lines 2x – 3y + k = 0, 3x – 4y – 13 = 0 and 8x – 11y – 33 = 0 are concurrent, is

λ

3 x - 4 y - 13 = 0, 8 x - 11 y - 33 = 0

2 x - 3 y + λ = 0

The value of $λ$ for which the lines 3x – 4y – 13 = 0, 8x – 11y – 33 = 0 and 2x – 3y + $λ = 0$ are concurrent is

2 x + 3 y - 13 = 0

x - 4 y + 10 = 0

a x + 5 y - 21 = 0

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