(A) Let the lines be $L_1: 2x + 3y - 4 = 0$ and $L_2: 6x + 9y + 8 = 0$. First,observe that $L_2$ can be written as $3(2x + 3y) + 8 = 0$. Substitute th

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The point lies outside the lines.

(A) Let the lines be $L_1: 2x + 3y - 4 = 0$ and $L_2: 6x + 9y + 8 = 0$. First,observe that $L_2$ can be written as $3(2x + 3y) + 8 = 0$. Substitute the point $(8, -9)$ into the expressions: For $L_1(8, -9) = 2(8) + 3(-9) - 4 = 16 - 27 - 4 = -15$. For $L_2(8, -9) = 6(8) + 9(-9) + 8 = 48 - 81 + 8 = -25$. Since both $L_1(8, -9)$ and $L_2(8, -9)$ have the same sign (both are negative),the point $(8, -9)$ lies on the same side of both lines. Therefore,the point lies outside the region between the two parallel lines.

Class 11 Mathematics Straight Line Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

Medium

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

A
The point lies outside the lines.
B
The point lies on the lines.
C
The point lies between the lines.
D
The point lies below one line and above the other.

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Straight Line

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Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

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EasyTS EAMCET 2023

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

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If $P_1$ and $P_2$ are the lengths of the perpendiculars from the origin to the lines $x \sec \theta + y \csc \theta = a$ and $x \cos \theta - y \sin \theta = a \cos 2\theta$ respectively,then what is the value of $4P_1^2 + P_2^2$?

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