The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line 3x + y = 1 is

(a) $y + 2 = 0, 3 x – y – 2 - 3 \sqrt[]{3} = 0$

(b) $x – 2 = 0, 3 x – y + 2 + 3 \sqrt[]{3} = 0$

(c) $3 x – y – 2 - 3 \sqrt[]{3} = 0$

(d) None of these

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1 Answer

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Vishal Baghel | Contributor-Level 10

3 months ago

This is a Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} E q u a t i o n o f l i n e i s g i v e n b y \\ \sqrt[]{3} x + y + 1 = 0 \\ \Rightarrow y = - \sqrt[]{3} x - 1 \\ ∴ S l o p e o f t h i s l i n e, m_{1} = - \sqrt[]{3} \\ L e t m_{2} b e t h e s l o p e o f t h e r e q u i r e d l i n e \\ ∴ t a n θ = | \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} | \\ \Rightarrow t a n 6 0^{0} = | \frac{- \sqrt[]{3} - m_{2}}{1 + (- \sqrt[]{3}) m_{2}} | \\ \Rightarrow \sqrt[]{3} = \pm (\frac{- \sqrt[]{3} - m_{2}}{1 - \sqrt[]{3} m_{2}}) \\ \Rightarrow \sqrt[]{3} = \frac{- \sqrt[]{3} - m_{2}}{1 - \sqrt[]{3} m_{2}} [T a k i n g (+) s i g n] \\ \Rightarrow \sqrt[]{3} - 3 m_{2} = - \sqrt[]{3} - m_{2} \\ \Rightarrow 2 m_{2} = 2 \sqrt[]{3} \Rightarrow m_{2} = \sqrt[]{3} \\ a n d \sqrt[]{3} = - (\frac{- \sqrt[]{3} - m_{2}}{1 - \sqrt[]{3} m_{2}}) [T a k i n g (-) s i g n] \\ \Rightarrow \sqrt[]{3} = \frac{\sqrt[]{3} + m_{2}}{1 - \sqrt[]{3} m_{2}} \\ \Rightarrow \sqrt[]{3} - 3 m_{2} = \sqrt[]{3} + m_{2} \\ \Rightarrow 4 m_{2} = 0 \Rightarrow m_{2} = 0 \\ ∴ E q u a t i o n o f l i n e t h r o u g h t h e (3, - 2) w i t h s l o p e \sqrt[]{3} i s \\ y + 2 = \sqrt[]{3} (x - 3) \\ \Rightarrow y + 2 = \sqrt[]{3} x - 3 \sqrt[]{3} \\ \Rightarrow \sqrt[]{3} x - y - 2 - 3 \sqrt[]{3} = 0 \\ a n d t h e e q u a t i o n o f l i n e t h r o u g h t h e (3, - 2) w i t h s l o p e 0 i s \\ y + 2 = 0 (x - 3) \Rightarrow y + 2 = 0 \\ H e n c e, t h e c o r r e c t o p t i o n i s (a) . \end{array}$

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The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line 3x + y = 1 is

(a) $y + 2 = 0, 3 x – y – 2 - 3 \sqrt[]{3} = 0$

(b) $x – 2 = 0, 3 x – y + 2 + 3 \sqrt[]{3} = 0$

(c) $3 x – y – 2 - 3 \sqrt[]{3} = 0$

(d) None of these

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The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line 3x + y = 1 is (a) y + 2 = 0 , 3 x – y – 2 - 3 3 = 0 (b) x – 2 = 0 , 3 x – y + 2 + 3 3 = 0 (c) 3 x – y – 2 - 3 3 = 0 (d) None of these

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The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line 3x + y = 1 is

(a) $y + 2 = 0, 3 x – y – 2 - 3 \sqrt[]{3} = 0$

(b) $x – 2 = 0, 3 x – y + 2 + 3 \sqrt[]{3} = 0$

(c) $3 x – y – 2 - 3 \sqrt[]{3} = 0$

(d) None of these