Question

If the straight line drawn through the point $P(\sqrt{3},2)$ & making an angle $\frac{\pi }{6}$ with the x-axis, meets the line $\sqrt{3}x-4y+8=0$ at $Q.$ Find the length $PQ.$

• A. $6$ units
• B. $8$ units
• C. $3\sqrt{3}$
• D. $6\sqrt{3}$

Answer 1

Answer: (A)

$6$ units

Given,
Straight line passes through P$(\sqrt{3},2)$ and makes an angle of $\frac{\pi }{6}$ with x-axis.

It meets the line $\sqrt{3}x-4y+8=\mathrm{0...1}$ at Q.

Equation of straight line is given by $\frac{y-2}{x-\sqrt{3}}=\frac{1}{\sqrt{3}}$

$y-2=\frac{1}{\sqrt{3}}(x-\sqrt{3})...2$

Q is given by solving both lines $1)$ and $2)$ which comes out be $(4\sqrt{3},5)$ .

Distance between them is given by $\sqrt{{(4\sqrt{3}-\sqrt{3})}^2+{(5-2)}^2}=6$ units.