SOLUTION: A straight line is drawn through the point (3,4). the line cuts the axes at the points A and B such that the area of the triangle OAB is 24. Find the x-intercepts of all such lines

Algebra ->  Length-and-distance -> SOLUTION: A straight line is drawn through the point (3,4). the line cuts the axes at the points A and B such that the area of the triangle OAB is 24. Find the x-intercepts of all such lines      Log On


   



Question 186467: A straight line is drawn through the point (3,4). the line cuts the axes at the points A and B such that the area of the triangle OAB is 24. Find the x-intercepts of all such lines
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the x-intercept x%5Bi%5D
Call the y-intercept y%5Bi%5D
Call the slope m
%281%2F2%29%2Ax%5Bi%5Dy%5Bi%5D+=+24
x%5Bi%5Dy%5Bi%5D+=+48
y%5Bi%5D+=+48%2Fx%5Bi%5D
and
m+=+-%28y%5Bi%5D%2Fx%5Bi%5D%29
m+=+-+%2848%2F%28x%5Bi%5D%29%5E2%29
The general equation is
y+=+mx+%2B+b and goes through (3,4)
and b is the y-intercept
4+=+m%2A3+%2B+b
4+=+3m+%2B+y%5Bi%5D
4+=+-3%2A%2848%2F%28x%5Bi%5D%29%5E2%29+%2B+y%5Bi%5D
4+=+-3%2A%2848%2F%28x%5Bi%5D%29%5E2%29+%2B+48%2Fx%5Bi%5D
4%2A%28x%5Bi%5D%29%5E2+=+-144+%2B+48x%5Bi%5D
4%2A%28x%5Bi%5D%29%5E2+-+48x%5Bi%5D+%2B+144+=+0
%28x%5Bi%5D%29%5E2+-+12x%5Bi%5D+%2B+36+=+0
%28x%5Bi%5D+-+6%29%5E2+=+0
x%5Bi%5D+=+6
The x-intercept is 6 answer
and
y%5Bi%5D+=+48%2Fx%5Bi%5D
y%5Bi%5D+=+48%2F6
y%5Bi%5D+=+8
check:
%281%2F2%29%2Ax%5Bi%5Dy%5Bi%5D+=+24
%281%2F2%29%2A6%2A8+=+24
24+=+24
m+=+-%28y%5Bi%5D%2Fx%5Bi%5D%29
m+=+-%288%2F6%29
m+=+-%284%2F3%29
The general equation is:
y+=+-%284%2F3%29%2Ax+%2B+8
does it go through (3,4)?
4+=+-%284%2F3%29%2A3+%2B+8
4+=+-4+%2B+8
4+=+4
OK