JEE Advanced Straight Lines & Pair of Straight Lines – Various Forms of Equation of a Line

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Q 1 :

A straight line $L$ through the point $(3, - 2)$ is inclined at an angle $60 °$ to the line $\sqrt{3} x + y = 1$ . If $L$ also intersects the $x$ -axis, then the equation of $L$ is [2011]

$y + \sqrt{3} x + 2 - 3 \sqrt{3} = 0$
$y - \sqrt{3} x + 2 + 3 \sqrt{3} = 0$
$\sqrt{3} y - x + 3 + 2 \sqrt{3} = 0$
$\sqrt{3} y + x - 3 + 2 \sqrt{3} = 0$

(2)

Let the slope of line $L$ be $m$ . Then

$| \frac{m + \sqrt{3}}{1 - \sqrt{3} m} |$ $= \sqrt{3}$

[IMAGE 293]

$\Rightarrow m + \sqrt{3} = \pm (\sqrt{3} - 3 m)$

$\Rightarrow 4 m = 0 or 2 m = 2 \sqrt{3} \Rightarrow m = 0 or m = \sqrt{3}$

$∵$ $L intersects x -axis,$ $∴$ $m = \sqrt{3}$

$∴$ $Equation of L is y + 2 = \sqrt{3} (x - 3)$

$\Rightarrow \sqrt{3} x - y - (2 + 3 \sqrt{3}) = 0$

Q 2 :

Let $P S$ be the median of the triangle with vertices $P (2, 2), Q (6, - 1)$ and $R (7, 3)$ . The equation of the line passing through $(1, - 1)$ and parallel to $P S$ is [2000]

$2 x - 9 y - 7 = 0$
$2 x - 9 y - 11 = 0$
$2 x + 9 y - 11 = 0$
$2 x + 9 y + 7 = 0$

(4)

$S$ is the midpoint of $Q$ and $R$

$∴$ $S \equiv (\frac{7 + 6}{2}, \frac{3 - 1}{2}) = (\frac{13}{2}, 1)$

[IMAGE 294]

$Now slope of P S = \frac{2 - 1}{2 - \frac{13}{2}} = - \frac{2}{9}$

Now equation of the line passing through $(1, - 1)$ and parallel to $P S$ is

$y + 1 = - \frac{2}{9} (x - 1) \Rightarrow 2 x + 9 y + 7 = 0$

Topic Question Set

Q 1 :

A straight line $L$ through the point $(3, - 2)$ is inclined at an angle $60 °$ to the line $\sqrt{3} x + y = 1$ . If $L$ also intersects the $x$ -axis, then the equation of $L$ is [2011]

Q 2 :

Let $P S$ be the median of the triangle with vertices $P (2, 2), Q (6, - 1)$ and $R (7, 3)$ . The equation of the line passing through $(1, - 1)$ and parallel to $P S$ is [2000]

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Topic Question Set

Q 1 : A straight line L through the point (3, -2) is inclined at an angle 60° to the line 3x+y=1. If L also intersects the x-axis, then the equation of L is [2011]

Q 2 : Let PS be the median of the triangle with vertices P(2,2), Q(6,-1) and R(7, 3). The equation of the line passing through (1,-1) and parallel to PS is [2000]

Want Us to Email you About Special Offers & Updates?

Q 1 :

A straight line $L$ through the point $(3, - 2)$ is inclined at an angle $60 °$ to the line $\sqrt{3} x + y = 1$ . If $L$ also intersects the $x$ -axis, then the equation of $L$ is [2011]

Q 2 :

Let $P S$ be the median of the triangle with vertices $P (2, 2), Q (6, - 1)$ and $R (7, 3)$ . The equation of the line passing through $(1, - 1)$ and parallel to $P S$ is [2000]