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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

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