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The line parallel to the x-axis and passing through the intersection of the lines \( \Large ax+2by+3b=0\ and\ bx-2ay-3a=0 \), where \( \Large (a, b) \ne (0, 0) \), is

A) above the x-axis at a distance of \( \Large \frac{2}{3} \) from it.
B) above the x-axis at a distance of \( \Large \frac{3}{2} \) from it.
C) below the x-axis at a distance of \( \Large \frac{2}{3} \) from it.
D) below the x-axis at a distance of \( \Large \frac{3}{2} \) from it.

Correct Answer:




D) below the x-axis at a distance of \( \Large \frac{3}{2} \) from it.

Description for Correct answer:

Equation of a line passing through the intersection of lines

\( \Large ax+2by+3b=0\ and\ bx-2ay-3a=0 \) is

\( \Large \left(ax+2by+3b\right)+n \left(bx-2ay-3a\right)=0 \) ...(i)

Now, this line is parallel to x-axis so cofficient of x = 0

=> \( \Large a+nb=0 => n = -\frac{a}{b} \)

On putting this value in equation (i) we get

\( \Large b \left(ax+2by+3b\right)-a \left(bx-2ay-3a\right)=0 \)

=> \( \Large 2b^{2}y+3b^{2}+2a^{2}y+3a^{2}=0 \)

=> \( \Large 2 \left(b^{2}+a^{2}\right)y+3 \left(a^{2}+b^{2}\right) = 0 \)

=> \( \Large y = -\frac{3}{2} \)

Part of solved Straight lines questions and answers : >> Elementary Mathematics >> Straight lines

Comments

Similar Questions

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