Q : Find the equation of the pair of straight lines passing through
the point (2, 2) and perpendicular to the pair of lines 3x2 + 7xy + 2y2 = 0 solution : Given equation 3x2 + 7xy + 2y2 = 0 ------------(1)
Here a = 3, h= 7/2 , b = 2 , point (x1 , y1 ) = ( 2 , 2)
Required equation is
b(x - x
1 )
2 - 2h(x - x
1) ( y - y
1 ) + ( y - y
1 )
2 = 0
implies 2(x - 2)
2 - 7 ( x - 2) ( y - 2) + 3( y - 2)
2 = 0
implies 2{x
2 - 4x + 4 } - 7 { xy - 2x - 2y + 4 } + 3( y
2 -4y + 4 ) = 0
implies 2x
2 - 8x + 8 - 7xy + 14x +14y - 28 + 3y
2 - 12y + 12 = 0
implies 2x
2 - 7xy + 3y
2 + 6x + 2y - 8 = 0 is the required equation