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Solved Examples - Tangent Normals
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This lesson takes up problems on tangents and normals

Vineet Loomba is teaching live on Unacademy Plus

Vineet Loomba
IITian | Best Online Maths Educator | Highest Overall Watch Time | 8+ Years Experience | Youtube: Maths Wallah | vineetloomba.com

U
Unacademy user
You are welcome. Pls share in circles as well
thnx sir for adding lenght of tangents also
AD
sir samaj nhi iyi
Vineet Loomba
5 months ago
Kya nhi aya smjh
yes sir please add that length of tangent lesson
Vineet Loomba
10 months ago
Okay
Shubh Gaur
10 months ago
thank you sir really means a lot
Vineet Loomba
10 months ago
Added today
Shubh Gaur
10 months ago
thanks sir
Sir Please make a video on finding the length of Tangent , Subtangent and Subnormal.
  1. SOLVED EXAMPLES APPLICATIONS OF DERIVATIVES JEE MAIN RANK BOOSTER COURSE PREPARED BY: ER. VINEET LOOMBA ITIAN IIT-JEE MENTOR


  2. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B.Tech. From IIT Roorkee -$ IIT-JEE Mentor Since 2010. Youtube Channel with 10k Active Followers & Founder @ vineetloomba.com * Follow me @ https://unacademy.com/user/vineetloomba to get unacademy updates or search me on Google * Share among your peers as SHARING is CARING!!


  3. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Other Detailed Courses Made so far on Unacademv: V Strategy for JEE Main and Advanced V Sets, Relations and Functions V Trigonometry V Applications of Derivatives Limits, Continuity. Differentiability V Indefinite Integration Definite Integration Complex Number V Logarithmic Functions V Sequences Series V Most Important Questions in IIT-JEE Permutations Combinations Binomial Theorem V Straight Lines V Applications of Integrals MathematicS V Parabola (Detailed Course) v Inverse Trigonometry V Mathematical Reasoning V Ellipse (Detailed Course) V Hyperbola V Differential Equations Circles (Detailed Course) V Probability Upcoming Courses next month: Coordinate Geometry > Differential Equations ER. VINEET LOOMBA (IIT RooRKee) MATHEMATICS FOR IIT-I


  4. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. The point of the curve 3x2- y2 8 at which the normal is parallel to the line x+ 3y 4is (B) (2,t2) So Here 3x2 - y2-8 dy dx dy 3x dx y 6x- .. slope of normal y/3x slope of given line-1/3 Since normal is parallel to the given line, therefore-y/3x--1/3 y-x Putting this value of y in the equation of the curve, we get x2 and y -+2 So required point is ( +2, +2) Ans.[B] SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT RooRKEE)


  5. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. f tangent line drawn to the curve x = at2, y = 2at is perpendicular to x-axis, then point of contact is. 1 2at and = 2-dy= Since tangent line is perpendicular to x axis, then Sol, [Slope of tangent at the point (at2, 2at)I dX Zat dy dx Therefore required point = (0, 0) Ans.[A] SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT RooRKEE)


  6. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. The angle of intersection of the curves y-4-x2 and y# x2 is (A) /2 (B) tan1 (4/3) (C) tan-1 (4217)(D) None of these Sol. Solving the give equations, we get ( 2) Now point of intersection y -4- x2 2 .. at ( J2.2 dy dy So required angle - tan-1 1+(+2J2)( 2-12 tan-1 (4/2/7 Ans.[C] = SUCCESS IN EE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT RooRKEe)


  7. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. The length of tangent to the curve x = a (cos t + log tan t/2), y= a sin t at any point is- (A) a (B) ax (C) ay (D) xy dx But dt 0 dx dt dt a l-sint+ sec2 (t/2) tan t/2 sin tsin- and a cos t dt dy (a cost) sin t dx = tan t a cos t :. Length of tangent a sin t1+tan2 t tan t dx a sint. sect Ans.[A] dx SUCCESS IN EE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT RooRKEe)


  8. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. If the length of the subnormal at any point of the cuve y a-n xn is constant, then n is equal o- (A) 2 (B) 1/2 (C) -1 (D)-1/2 dy dx Sona1-n x-1, so at any point dy Length of subnorma y dx = (al-n Xn) (nal-n Xn-1) = na2 (1-n) x2n_1 It will be constant when 2n-1 = 0 i.e., when n = 112. Ans. B SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT RooRKEE)


  9. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. The slope of tangent at (2, -1) to the curve x t23t -8 and y 2t2 -2t 5 is- (A) -6 (B) 0 (C) 6/7 (D) 22/7 Sol. xt23t82t3 dt dy dt dy 4t 2 dx 2t3 Since (2,-1) is a point on the curve therefore 2 = t2 + 3t-8 5 2 and-I = 2t2-2t-5 t = 2,-1 Thus t=2 Now slope of tangent at the given point 4x2-2 6 2x2 +3 7 Ans.[C] SUCCESS IN EE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT RooRKEe)


  10. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ENROL for this Course (Free) Enroll 439 Recommend Lessons (Like) E Rate and Review the Course .Comments . Sharing with friends 15 1. 68 111 ratings 21 reviews Share ER. VINEET LOOMBA (IIT RooRKEE) MATHEMATICS FOR IIT-IEE