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find the angle between the two st lines 3x=4y+7 and 5y=12x+6 and also the equations to the two lines which pass through the point (4,5) and make equal angles with the two given lines

 
find the angle between the two st lines 3x=4y+7 and 5y=12x+6 and also the equations to the two lines which pass through the point (4,5) and make equal angles with the two given lines

Grade:12th pass

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below,
4y = 3x - 7........(1)
5y = 12x + 6........(2)
m_{1} = \frac{3}{4}, m_{2} = \frac{12}{5}
Angle between line 1 & 2
tan\theta = |\frac{m_{1}-m_{2}}{1+m_{1}m_{2}}|
tan\theta = |\frac{\frac{3}{4}-\frac{12}{5}}{1+\frac{3}{4}.\frac{12}{5}}|
tan\theta = |\frac{15-48}{20+36}|
tan\theta = \frac{33}{56}
\theta = tan^{-1}\frac{33}{56}
Let the slope of the line be ‘m’
\frac{m-\frac{3}{4}}{1+m.\frac{3}{4}} =\pm \frac{m-\frac{12}{5}}{1+m.\frac{12}{5}}
(4m-3)(12m+5) = \pm (3m+4)(5m-12)
(48m^{2}-16m-15)= \pm (15m^{2}-16m-48)
+ sign is not possible.
48m^{2}-16m-15= -15m^{2}+16m+48
63m^{2}-32m-63= 0
m = \frac{-7}{3}, \frac{3}{7}
Line equations:
(y-5) = \frac{-7}{3}(x-4)
(y-5) = \frac{3}{7}(x-4)
Jitender Singh
13 Points
9 years ago
Hello Student,
There is a small mistake in the above answer.
Sorry about that
m = -7/9, 9/7

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