Straight Lines
Board: CBSE |Class:Class11
ComprehensivestudynotesforStraightLinesbyAjayYadav(MathKingofKatargam).
Slopem=tanθ=(y₂-y₁)/(x₂-x₁).Slopeoflineparalleltox-axis=0.Verticallineslopeisundefined.
Slope-intercept:y=mx+c.Point-slope:y-y₁=m(x-x₁).Two-point:(y-y₁)/(y₂-y₁)=(x-x₁)/(x₂-x₁).Intercept:x/a+y/b=1.Normal:xcosω+ysinω=p.
ax+by+c=0.Slope=-a/b.Distancefromorigin=|c|/√(a²+b²).
tanθ=|(m2-m1)/(1+m1m2)|.Linesareparallelifm₁=m₂.Perpendicularifm₁m₂=-1.
Distancebetweenpoint(x₁,y₁)andlineax+by+c=0:d=|ax1+by1+c|/√(a²+b²).Distancebetweenparallellinesax+by+c₁=0andax+by+c₂=0:d=|c2-c1|/√(a²+b²).
| Slope | m=(y₂-y₁)/(x₂-x₁) |
| Point-Slope | y-y₁=m(x-x₁) |
| Intercept | x/a+y/b=1 |
| Anglebetweenlines | tanθ=|(m2-m1)/(1+m1m2)| |
| Point-line distance | d = |ax1+by1+c|/√(a²+b²) |
Example1:Findslopeoflinethrough(1,2)and(3,6).
Solution:m=(6-2)/(3-1)=4/2=2.
Example2:Findequationoflinewithslope2through(1,3).
Solution:y-3=2(x-1)⇒y=2x+1.
Example3:Finddistanceofpoint(1,2)fromline3x+4y-6=0.
Solution:d=|3+8-6|/√9+16 = 5/5 = 1 unit.
Practice Questions
- Find equation of line through (2,3) and (4,7).
- Are lines 2x+3y=5 and 4x+6y=12 parallel?
- Find the angle between y = 2x+1 and y = -x/2+3.
- Find the foot of perpendicular from (1,2) to line 2x+3y=6.
- Find distance between parallel lines 3x+4y=5 and 3x+4y=15.
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