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Grade 12th passDiscuss with colleagues and IITians

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

Tejas Jaiswal

11 Years agoGrade 12th pass

2 Answers

Jitender Singh

11 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

11 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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