Question

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

• A. 1 and 2 only
• B. 2 and 3 only
• C. 1 and 3 only
• D. 1, 2 and 3

Answer 1

The correct option is B 2 and 3 only

Distance of the point $(a,b)$ from the line $8x+6y+1=0$ is equal to $1$ unit

$\therefore \left|\frac{8a+6b+1}{\sqrt{8^2+6^2}}\right|=1$

$\therefore \frac{8a+6b+1}{\sqrt{8^2+6^2}}=\pm 1$

$\therefore \frac{8a+6b+1}{10}=\pm 1$

$\therefore 8a+6b+1=\pm 10$

$\therefore 8a+6b-9=0$

or

$\therefore 8a+6b+11=0$

So, the answer is option (B)