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Sub-tangent and Sub-Normal
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Length of Sub-tangent and Sub-normal along with length of Tangent and Normal has been explained in this lesson

Vineet Loomba is teaching live on Unacademy Plus

Vineet Loomba
IITian | No. 1 Educator in IIT-JEE (Maths) | 550+ free Lessons | 8+ Years Experience |vineetloomba.com | Youtuber | Read Reviews!!
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Sir will you please add Mean value theorems( like LMVT etc.) also in this course??
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  1. IIT-JEE VIDEO COURSE FOR SURE SHOT SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) IIT-JEE MATHS MADE EASY PREPARED BY: ER. VINEET LOOMBA IITian | IIT-JEE MENtOR Search vineet loomba unacademy" on GOOGLE


  2. REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B.Tech. From IIT Roorkee IIT-JEE Mentor Since 2010 Doubts/Feedback in Comment Section * Comment other topics you want to revise. Follow me @ https://unacademy.com/user/vineetloomba to get updates or search me on Google * Share among your peers as SHARING is CARING!!


  3. APPLICATION OF DERIVATIVES SUB-TANGENT ! SUB-NORMAL IIT-IEE MATHS MADE EASY PREPARED BY: ER. VINEET LOOMBA IITiAN | IIT-JEE MENTOR FoR SURE SHoT SUcCESS IN JEE MAIN AND ADVANCED (IIT-JEE)


  4. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) (a) Length of tangent PT y cosec 0 2 dy dx y/ P/(x, y) Tangent/ O Normal TO Subtangent Subnormal MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  5. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) (b) Length of Normal PN ly sec 0 v1(y)2 P/(x, y) Tangent/ O Normal TO Subtangent Subnormal MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  6. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) (c) Length of sub tangent TM ly cot 0 lyly' Pl(x, y) Tangen 0 Normal TO MN Subtangent Subnormal MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  7. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) (d) Length of subnormal MN ly tan 0lyy' Pr(x, y) angen Normal TO M N Subtangent Subnormal MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  8. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. Find the nh angent, subtangent, normal and subnormal at the point (2,4) of the curve y 8x. Sol Differentiating the equation of the curve w.r.t. x, we get dy dx dy d24)44 1 Therefore at the point (2,4) length of tangent length of sub tangent 4/14 length of normal 41+(1 4 2 length of sub normal 4.14 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  9. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. Find the length of tangent, sub-tangent, normal and sub-normal at the point e of the curve a (e+ sin ), and y dy) x a(1-cos ) (dy/de) a sin a(1+cos Sol.dx dy dx 2 sin /2 cos /2 2 cos 2 /2 2 a sin- / 2 sec /2 sine/2 .. length of tangent a (1 -cos )V1+tan2 /2- a. sin /2 tan /2 cos / 2 length of normal-a (1-cos, 11+tan 2 /2-a.2 sin2 /2. sec /2 a (1-cos ) tan /2 2a sin2 /2 sin /2 cos 0/2 length of sub tangent = -a sin length of sub normal a (1-cos ) tan /2 2a sin2 /2 tan /2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)


  10. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B.Tech. From IIT Roorkee IIT-JEE Mentor Since 2010 Doubts/Feedback in Comment Section * Comment other topics you want to revise. Follow me @ https://unacademy.com/user/vineetloomba to get updates. * Share among your peers as SHARING is CARING!!