# find the equation of a straight line passing through the point (4,5) and equally inclined to the lines 3x = 4y +7 and 5y = 12x +6 ?

SREEKANTH
85 Points
8 years ago
the line passing through the point=(4,5)
the line equally inclined to the lines 3x=4y+7,5y=12x+6  means the angle between the required line and the two lines is equalassume the slop of the required equation is m1
the slope of the equation 3x=4y+7=>y=(3x)/4-7/4 so the slope of the equation is ¾
the slope of the equation 5y=12x+6=>y=(12x)/5+6/5 so the slope of the equation is 12/5
when slope of the two equations are formula for finding the angle between them is
a=tan^-1(m1-m2)/1+m1m2=tan^-1(m1-m2)/1+m1m2
=tan^-1(m1-3/4)/1+3m1/4=tan^-1(m1-12/5)1+12m1/5)
=>(4m1-3)/(4+3m1)=(5m1-12)/(5+12m1)
=>(20m1+48m1^2-15-36m1=20m1+15m1^2-48-36m1)
=>m1^2=1
=>m1=+1   or -1
so the two equations incline the given ttwo equations equally
those are passing throught he point  (4,5) and having the slope 1  and   -1
those arey-x+1=0  and y+x-9=0
=>
sai hemanth kumar
57 Points
8 years ago
100y-77x=192
Raj Basfor
34 Points
6 years ago
1.Find slope m1 and m2 from both equation.
2. find tanx of m1
3.find tanx of m2
4.compare 2 and 3 and get, |4m-3|/|4+3m|=|5m-12|/|5+12m|.
5. Two 'm' values will come i.e is m=9/7,-7/9
7.y-5=-7/9(x-4) u will get 9y+7x-73=0
And similarly,
y-5=9/7(x-4) u will get 9x-7y=1.
Solved. I think u got ur answer.M not a IITian but 1 year to go to be an IITian.