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Analytical Geometry

Cool goIITian

 Joined: 9 Sep 2007 Post: 39
23 Oct 2007 12:50:53 IST
0 People liked this
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Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Analytical Geometry

(1) find the equations of lines which pass through (4,5)and makes equal angle with the lines 5y=12x+6&3x=4y+7.
(2)find the equation of third side of triangle if the equation of two sides be 3x-2y+6=0& 4x+7y+5=0and the orthocentre is (1,1)

Blazing goIITian

Joined: 1 May 2007
Posts: 2830
23 Oct 2007 14:06:32 IST
1 people liked this

1)

let the slope of the line be m.
The slopes of the given lines are 12/5 and 3/4. As they are equally inclined to the two unknown lines, we have
(m+12/5)/(1-12m/5) = -( m+3/4)/1-3m/4)

Solving for m we get m = 7/9 and m=-9/7

(Please notify me if my m values are wrong)

So putting these values in point slope formula, the equations are:

y-5 = 7/9(x-4)

and y-5=-9/7(x-4) are the two lines.

Scorching goIITian

Joined: 21 Oct 2007
Posts: 271
23 Oct 2007 14:24:10 IST
0 people liked this

2)
first draw the diagram
solve the given equations then u get one co ordinate of the side as u have orthocenter u get the slope of the line
as required equation of the line and above line is perpendicular so product of slopes is -1. then v get the slope of required line
nw we require one coordinate
let triangle be ABC , O orthocenter , D, E , F the points wer othocenter meets BC , CA , AB
let equation of AB be 3x-2y+6=0 n equation of AC be 4x+7y+5=0
OB is perp to AC we no slope of AC so we get of OB too
as OB passes throgh O we get the equation of OB
solvin OB n AB we get one coordinate of side then we have slope n coordinate we can find equation

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