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AP ICET 2024 6th May 2024 Shift 1

Question : 171 of 200

Marks: +1, -0

3x+4y+1=0

6x+8y-1=0

Solution:

The general formula for the distance between two parallel lines

ax+by+c_1=0

and

ax+by+c_2=0

is:

\; \text{ Distance }\; = \; \frac{|c_2-c_1|}{\sqrt{a^{2}b^{2}}}

For the lines

3x+4y+1=0

and

6x+8y-1=0

, the coefficients of

x

and

y

are proportional. The lines are parallel, so we can use the distance formula for parallel lines. Thus, the distance is :

\; \frac{|(-1)-1|}{\sqrt{3^{2}+4^{2}}} = \; \frac{2}{\sqrt{9+16}} = \; \frac{2}{5} = 0.3 .

Quick Tip

For parallel lines, the distance formula simplifies to

\frac{|c_2-c_1|}{\sqrt{a^{2}+b^{2}}}

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