The position of the point $(8, - 9)$ with respect to the lines $2 x + 3 y - 4 = 0$ and $6 x + 9 y + 8 = 0$ is

point lies on the same side of the lines

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point lies on one of the lines

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point lies on the different sides of the line

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point lies between the lines

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Solution

The correct option is A point lies on the same side of the lines
Given
$L_{1} : 2 x + 3 y - 4 = 0$
$(8, - 9) 16 - 27 - 4 = - 15 < 0$
$L_{2} : 6 x + 9 y + 8 > 0$
$(8, - 9) 48 - 81 + 8 = - 25 < 0$
Hence point lies on some side of the lines

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If the point $P (a, 5)$ lies on the line $2 x - 3 y - 5 = 0$ , then find the value of $a$ .

(- 8, 9)

2 x + 3 y - 4 = 0

6 x + 9 y + 8 = 0

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