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Angle of intersection of two curves
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This lesson explains the concept of angle of intersection of two curves using derivatives

## Vineet Loomba is teaching live on Unacademy Plus

Vineet Loomba
IITian | No. 1 Educator in IIT-JEE (Maths) | 3 Million Minutes Watch Time | 8+ Years Experience | Youtube: Maths Wallah | vineetloomba.com

compiler takes code written in a programming language as input and converts it to assembly code as output which is passed as input to the assembler which converts it to object code as output which is stored on the harddisk of the computer.
Sweta Kumari
9 months ago
Very good... keep it up
Sumeet Lalla
9 months ago
thank you
Sweta Kumari
9 months ago
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Sumeet Lalla
9 months ago
sure thank you
Sumeet Lalla
9 months ago
hello maam, sorry could not register for the above in the given timeframe sincere apologies for the same
Sweta Kumari
9 months ago
it's ok..
sir B point ko apne at1 ka square, at1 ka cube kaise mana
Vineet Loomba
4 months ago
Parametric points hote h n ye ...class 11 me conic me pdhte h
Elima sharma
4 months ago
ok sir
nice sir Thanks a lot
Is subtangent topic is includeed in JEEMAINS Syllabus?/
Sir, ek bhut bari confusion h 1st quest me.......yh kh aapne point B(at1²,at1³) hi Q liya sir......kya hm (x1,y1) assume ni krskte h??? Maine try kiya but ans ni aa rha h:-(.... aur agar liya bhi toh [a1(t1²),a1(t1)³] Q ni liya sir???.... How did you tell me to clarify my doubt ?? ??? ........
Vineet Loomba
8 months ago
nhi ... ye coordinate geometry se ata h ...parametric point assume krna. .. idhar toh uski apllication hai
Sidra Hassan
8 months ago
oooo....okay sir thanx..
Sir in the 1st question how did u decide the B points .As we can take it as x and y ryt ,but u took it in terms of a ..???? Hoe will u find it ?
Vineet Loomba
9 months ago
that is the parametric points of the curve ...u must have learnt the method in coordinate Geomtery
Have u made a video on this topic ?
Vineet Loomba
9 months ago
not yet ..but i will make in next courses
ok thank you sir
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 TANGENTS AND NORMALS 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) Illustration The tangent to X3 = ay' at the point A (at, at3, meets the curve against at the points : at at at at (A) 4 8 (C) (4a2, 8a) (B) 48 (D) (4at,-8at') SOLUTION (B) Equation of tangent to : x = at, v = af is 3 at a (-) t+ t at y-at(x at) at Let B(at,at) be the point where it again meets the curve Hence the meeting point B is Slope oftangent at A= slope of/18 at-at MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

5. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ANGLE OF INTERSECTION OF TWO CURVES If two curves y - f,(x) and y x) intersect at a point P, then the angle between their tangents at P is defined as the angle between these two curves at P. But slopes of tangents at P aand intersection (0) is given by nts at P are( ),ard ( ),.so at p tat arge of . so (dy/dx), -(dy/dx)2 1+(dy/dx)1(dy/dx)2 tan = The other angle of intersection will be (180 - Note : If two curves intersect orthogonally i.e. at right angle then so the condition will be 2 dy) (dy MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

6. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) The angle of intersection between the curves y = x and y2= 4x at (4.4) (1) tan-l Ex. (2) tan-1 2 4 2 Sol.(3) Differentiating given equation, we have dy1 and dy .. at (4, 4) dx1 2 Hence angle of intersection tan1 tan (1/3) 1+1 2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

7. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. The condition that the curves-1 and xy mutually intersect orthogonally is (1) a2 + b2-o (2) a2 b2 (3) a2b20 (4) a2 =-2 Sol.(2) The given curves are and xy c2 from (a) bx (1) and (2) intersect orthogonally if and from (2), dy dy dy a2 b2which is the required condition. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

8. 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!!