SOLUTION: Write the equation of the line which passes through the point of intersection of the lines x-2y-4 = 0 and 4x-y-4 = 0 and satisfying the additional conditions a) parallel to the l

Algebra ->  Circles -> SOLUTION: Write the equation of the line which passes through the point of intersection of the lines x-2y-4 = 0 and 4x-y-4 = 0 and satisfying the additional conditions a) parallel to the l      Log On


   

Question 872791: Write the equation of the line which passes through the point of intersection of the lines x-2y-4 = 0 and 4x-y-4 = 0 and satisfying the additional conditions
a) parallel to the line 16x -11y +3 =0
b) perpendicular to the line 9x + 22y - 8 =0
Can you please help me out? Thanks so much in advance:)
Found 2 solutions by mananth, josmiceli:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation of the line which passes through the point of intersection of the lines x-2y-4 = 0 and 4x-y-4 = 0 and satisfying the additional conditions
a) parallel to the line 16x -11y +3 =0
b) perpendicular to the line 9x + 22y - 8 =0


Solve x-2y-4 = 0 and 4x-y-4 = 0
to get (x,y)
1 x -2 y = 4 .............1

4 x -1 y = 4 .............2
Eliminate y
multiply (1)by 1
Multiply (2) by -2
1 x -2 y = 4
-8 x + 2 y = -8
Add the two equations
-7 x = -4
/ -7
x = 1
plug value of x in (1)
1 x -2 y = 4
1 -2 y = 4
-2 y = 4 -1
-2 y = 3
y = -2

(1,-2) is the point of intersection
16 x -11 y = -3
Find the slope of this line
make y the subject
-11 y = -16 x -3
Divide by -11
y = 1 4/9 x + 2/7
Compare this equation with y=mx+b
slope m = 1 4/9
The slope of a line parallel to the above line will be the same
The slope of the required line will be 1 4/9
m= 1 4/9 ,point ( 1 , -2 )
Find b by plugging the values of m & the point in
y=mx+b
-2 = 16/11 + b
b= -3.45
m= 13/9
Plug value of the slope and b in y = mx +b
The required equation is y = 13/9 x -38/11

for perpendicular take the negative reciprocal of the slope of given line 9x + 22y - 8 =0
and point is (1,-2)
frame the equation

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find the (x,y) location of the intersection
of the lines:
(1) +x+-+2y+-+4+=+0+
(2) +4x+-+y+-+4+=+0+
--------------------------
Multiply (1) by +4+ and
subtract (1) from (2)
(2) +4x+-+y+-+4+=+0+
(1) +-4x+%2B+8y+%2B+16+=+0+
------------------------------
+7y+%2B+12+=+0+
+y+=+-12%2F7+
----------------------
Plug this back into (1) or (2)
(1) +x+-+2%2A%28-12%2F7%29+-+4+=+0+
(1) +x+%2B+24%2F7+-+28%2F7+=+0+
(1) +x+-+4%2F7+=+0+
(1) +x+=+4%2F7+
The intersection is at ( 4/7, -12/7 )
--------------------------------------
(a) Find the slope of this line
+16x+-+11y+%2B+3+=+0+
+11y+=+16x+%2B+3+
+y+=+%2816%2F11%29%2Ax+%2B+3%2F11+
The slope is +16%2F11+
----------------------------
You can use the point-slope formula
+%28+y+-+%28-12%2F7%29+%29+%2F+%28+x+-+4%2F7+%29+=+16%2F11+
+y+%2B+12%2F7+=+%28+16%2F11+%29%2A%28+x+-+4%2F7+%29+
+y+%2B+12%2F7+=+%2816%2F11%29%2Ax+-+%2816%2F11%29%2A%284%2F7%29+
Multiply both sides by +77+
+77y+%2B+11%2A12+=+7%2A16%2Ax+-+4%2A16+
+77y+=+112x+-+132+-+64+
+77y+=+112x+-+196+
+112x+-+77y+-+196+=+0+
------------------------------------
That's it unless I made a mistake.
That's all I have time for