Question

April 20
(vi) 5x + 2y + 11 = 0 and 5x - 3y + 9 = 0 find the angle between them​

Answer 1

Answer:

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Answer 2

Given data :

The two straight lines are

• $5x + 2y + 11 = 0$ _____ (1)
• $5x - 3y + 9 = 0$ _____ (2)

To find :

The angle between the lines (1) and (2).

Step-by-step explanation :

Write the equations in the form y = mx + b :

Equation (1) and (2) can be written as

• $y=-\frac{5}{2}x-11$
• $y=\frac{5}{3}+3$

Finding slopes of the given lines :

The slopes of the given lines are

• $m_{1}=-\frac{5}{2}$
• $m_{2}=\frac{5}{3}$

Finding angles between the lines :

If $\theta$ be the angle between the given lines, then

• $\quad tan\theta=|\frac{-\frac{5}{2}-\frac{5}{3}}{1+(-\frac{5}{2})\frac{5}{3}}|$

• $=|\frac{-\frac{5}{2}-\frac{5}{3}}{1-\frac{25}{6}}|$

• $=|\frac{\frac{-15-10}{6}}{\frac{6-25}{6}}|$

• $=|\frac{-25}{-19}|$

• $\Rightarrow tan\theta=\frac{25}{19}$

• $\Rightarrow \theta=tan^{-1}(\frac{25}{19})$

Answer :

The angle between the given two lines is $tan^{-1}(\frac{25}{19})$.