A line inclined at an angle of 135° 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 √2. The coordinates of P and Q are respectively.

Question

A line inclined at an angle of 135° 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 √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)

Tardigrade Admin · Accepted Answer

(x-3/ cos θ)=(y-4/ sin θ)=± 2 √2 ⇒ x=3 ± 2 √2 cos θ and y=4 ± 2 √2 sin θ, θ=135°

Q. A line inclined at an angle of $13 5^{\circ}$ to the $x$ -axis passes through the point $A (3, 4)$ . There are two points $P$ and $Q$ on the line such that $A P = A Q = 22$ . The coordinates of $P$ and $Q$ are respectively.

(-1, -6) and (5, 2)

(1, -6) and (-5, 2)

(1, 6) and (5, -2)

(1, 6) and (5, 2)

$\frac{x - 3}{c o s θ} = \frac{y - 4}{s i n θ} = \pm 22$
$\Rightarrow x = 3 \pm 22 cos θ$
and $y = 4 \pm 22 sin θ, θ = 13 5^{\circ}$

Q. A line inclined at an angle of 135∘ 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=22​. The coordinates of P and Q are respectively.