First slide

Equation of line in Straight lines

Question

A straight line L is drawn through the point A(2, 1) is such that its point of intersection with x + y = 9 at distance of $3 \sqrt{2}$ from A. Then angle made by L with positive direction of x-axis is

Moderate

A

$3 0^{0}$
B

$45^{0}$
C

$6 0^{0}$
D

$9 0^{0}$

Solution

A (2,1), $x + y - 9 = 0$ -------(1)
$r = 3 \sqrt{2}$
, $x = 2 + (3 \sqrt{2}) \cos θ$ , $y = 1 + (3 \sqrt{2}) \sin θ$
                 $(1) \Rightarrow 3 + 3 \sqrt{2} (\cos θ + \sin θ) = 9$
                 $1 + \sqrt{2} (\cos θ + \sin θ) = 3$
                 $\cos θ + \sin θ = \sqrt{2}$
                 $\frac{1}{\sqrt{2}} \cos θ + \frac{1}{\sqrt{2}} \sin θ = 1$
                 $\cos (θ - \frac{π}{4}) = \cos 0^{0}$
                 $θ = π / 4$

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