SATHEE: Straight Line and Pair of Straight Lines 2 Question 7

Straight Line and Pair of Straight Lines 2 Question 7

7. Find the equation of the line which bisects the obtuse angle between the lines $x - 2 y + 4 = 0$ and $4 x - 3 y + 2 = 0$ .

(1993, 2M)

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Answer:

Correct Answer: 7. $(4 + \sqrt{5}) x - (2 \sqrt{5} + 3) y + (4 \sqrt{5} + 2) = 0$

Solution:

Given equations of lines are

$x - 2 y + 4 = 0$ and $4 x - 3 y + 2 = 0$

Here, $a_{1} a_{2} + b_{1} b_{2} = 1 (4) + (- 2) (- 3) = 10 > 0$

For obtuse angle bisector, we take negative sign.

$\begin{array}{lc} ∴ & \frac{x - 2 y + 4}{\sqrt{5}} = - \frac{4 x - 3 y + 2}{5} \\ \Rightarrow & \sqrt{5} (x - 2 y + 4) = - (4 x - 3 y + 2) \\ \Rightarrow & (4 + \sqrt{5}) x - (2 \sqrt{5} + 3) y + (4 \sqrt{5} + 2) = 0 \end{array}$

Straight Line and Pair of Straight Lines 2 Question 7

7. Find the equation of the line which bisects the obtuse angle between the lines $x - 2 y + 4 = 0$ and $4 x - 3 y + 2 = 0$ .

Answer:

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Straight Line and Pair of Straight Lines 2 Question 7

7. Find the equation of the line which bisects the obtuse angle between the lines x−2y+4=0 and 4x−3y+2=0.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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7. Find the equation of the line which bisects the obtuse angle between the lines $x - 2 y + 4 = 0$ and $4 x - 3 y + 2 = 0$ .