~`$tr@ight Lines $ubjective Probs `~[CHALLENGING]

{2} Find the coords of the Orthocentre of a triangle of sides

x + y = 1
2x + 3y = 6
4x - y = 4

WITHOUT FINDING THE COORDS OF ITS VERTICES!!!

one way is take teh famiily of straight lines passing through the two lines of the triangle..

THen find the condition that they are perpendicular to the third line by seeing the slope..

In the same way find the equation of the second perpendicular..

SOlve them to get the equation of the Orthocenter

{6}A line is such that its segment b/w the lines 5x - y - 4=0 & 3x + 4y - 4=0 is bisected at

the point (1 ,5).Obtain the equation ?

Use the parametric form of the line passing through a point..

First point will be 1+r cos @, 5 + r sin @

Another point at equal distance will be 1-r cos@, 5 - r sin @

Now first point lies on 1st line, 2nd on second..

Solve teh two equations :)

{7} A line thru the point P (2,-3) meets the lines x-2y+7=0 and x+3y-3 = 0 at the points A

& B respectively.If P divides AB externally in the ratio 3:2 Find the eqn of AB ?

Use the same logic of the previous post... this time the distance will be r, 3/2r ?