## Vineet Loomba is teaching live on Unacademy Plus

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

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!!

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)

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)

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)

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)

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)

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!!