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October 30th, 2012, 08:46 AM  #1 
Newbie Joined: Oct 2012 Posts: 20 Thanks: 0  About Straight Lines Plz
find the equations of lines passing through (2,3) and making an intercept of length of SQRT OF 10 between the lines 2x+y3=0 and 2x+y4=0.

October 30th, 2012, 08:56 AM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 5  Re: About Straight Lines Plz
The two given lines, 2x+ y 3= 0 and 2x+ y 4= 0 are parallel which simplifies the problem greatly. Any line through (2, 3) can be written as y= m(x 2)+ 3 and so will intersect the first line when 2x+ [m(x 2)+ 3] 3= (m+2)x 2m= 0. You can find the x and y coordinates of the point of intersection (they will depend on m) from that. The line will intersect the second line when 2x+ [m(x 2)+ 3] 4= (m+2)x 2m1= 0. Find the coordinates of that point (again depending on m). Find the distance between the two points of intersection, as a function of m, set it equal to 10, and solve for m.


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