S=2x2+3xy−2y2−7x+y+3 =(x+2y−3)(2x−y−1) Equation line L1 drawn from (3,−4) on (x+2y−3) ⇒L1:(y+4)=2(x−3) Equation of line L2 drawn from (3,−4) on (2x−y−1) L2:(y+4)=−
1
2
(x−3)⇒L1:2x−y−10=0 L2:x+2y+5=0 Parallel distance between x+2y+5=0 and x+2y−3=0 is ⇒
|5+3|
√1+4
=
8
√5
Parallel distance between 2x−y−1=0 and 2x−y−10=0 ⇒