Question

A line inclined at an angle of $135^{\circ}$ to the $x$-axis passes through the point $A (3,4)$. There are two points $P$ and $Q$ on the line such that $AP = AQ =2 \sqrt{2}$. The coordinates of $P$ and $Q$ are respectively.

• A. (-1, -6) and (5, 2)
• B. (1, -6) and (-5, 2)
• C. (1, 6) and (5, -2)
• D. (1, 6) and (5, 2)

Answer 1

Answer: (D)

$\frac{x-3}{\cos \theta}=\frac{y-4}{\sin \theta}=\pm 2 \sqrt{2} $
$\Rightarrow x=3 \pm 2 \sqrt{2} \cos \theta$
and $y=4 \pm 2 \sqrt{2} \sin \theta, \theta=135^{\circ}$