Q207 / 270 · NDA 2016 (Phase 2) · Mathematics

If $(a, b)$ is at unit distance from the line $8 x+6 y+1=0$, then which of the following conditions are correct? 1. $3 a-4 b-4=0$ 2. $8 a+6 b+11=0$ 3. $8 a+6 b-9=0$ Select the correct answer using the code given below:

  • A
    1 and 2 only
  • Correct answer
    B
    2 and 3 only
  • C
    1 and 3 only
  • D
    1,2 and 3

Solution

Here $\frac{|8 a+6 b+1|}{\sqrt{8^2+6^2}}=1 \Rightarrow|8 a+6 b+1|=10$ $\begin{aligned} & \Rightarrow 8 \mathrm{a}+6 \mathrm{~b}+1= \pm 10 \\ & \Rightarrow 8 \mathrm{a}+6 \mathrm{~b}+1=10 \& 8 \mathrm{a}+6 \mathrm{~b}+1=-10 \\ & \Rightarrow 8 \mathrm{a}+6 \mathrm{~b}-9=0 \& 8 \mathrm{a}+6 \mathrm{~b}+11=0 \end{aligned}$

Hence, the correct answer is option: 'B'.

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