Question

If p be the length of the perpendicular from the origin on the straight line x + 2by = 2p ,then what is the value of b?

• A. $\frac{1}{p}$
• B. p
• C. $\frac{1}{2}$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

Answer: (D)

$\frac{\sqrt{3}}{2}$

Answer 2

Length of perpendicular from the origin on the straight line x + 2by - 2p = 0 is $\left|\frac{0+2b\times0-2p}{\sqrt{1^{2}+\left(2b\right)^{2}}} \right| = p$ or $p= \left|\frac{-2p}{\sqrt{1^{2}+4b^{2}}}\right|$ or $p^{2} = \frac{4p^{2}}{1+4b^{2}}$ $\Rightarrow \frac{4}{1+4b^{2}} = 1$ $\Rightarrow 1+4b^{2}=4$ or $4b^{2} = 3 \Rightarrow b^{2} = \frac{3}{4}$ $\Rightarrow b = \pm \frac{\sqrt{3}}{2} \Rightarrow b = \frac{\sqrt{3}}{2}$ matches with the given option.