Straight lines

Straight lines

1. Forms of equation of straight line

   • slope form y=mx+c
     • here m is slope and c is y intercept
   • point form (y-y1)=m(x-x1)
   • intercept form x/a + y/b =1
     • a is x intercept and b is y intercept

2. Locus

   • It is the path traced by a point when bounded by certain condition
   • To find it we have to follow some steps
     • 1 take the points h and k
       • Then apply the condition given in the question
         • Relate h and k by geometry or trigonometry
           • replace h and k by x and y

3. Pair of straight lines

   • General form
     • ax^2 +2hxy+by^2+2gx+2fy +c
       • Or when passing through origin then can be written as m1m2x^2+(m1+m2)xy+y^2
   • Angle between the pair of lines tan thita =(2(h^2-ab)^0.5)/(a+b)
     • If h^2>ab then two distinct lines
     • if h^2=ab then both lines are same
     • If h^2<ab then irreal lines
   • Angle bisector of pair of straight line (x^2-y^2)/(a-b)=xy/h
   • Let m1 m2 be slope of both straingt lines
     • m1+m2=-2h/b
       • m1m2=a/b
   • if a+b=0 then lines are perpendicular

4. Angle bisector between lines

   • ax+by+c/(a^2+b^2)^0.5=
     • If a1a2+b1b2>0
       • +ve is obtuse -ve is acute
     • If a1a2+b1b2<0
       • -ve Obtuse and +ve acute