## Vineet Loomba is teaching live on Unacademy Plus

STRAIGHT LINES MOST IMPORTANT QUESTIONS JEE MAIN RANK BOOSTER COURSE PREPARED BY: ER. VINEET LOOMBA ITIAN IIT-JEE MENTOR

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!!

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

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) IfA (1, p2);B (0, 1) and C (p, 0) are the coordinates of three points then the value of p for which the area of the triangle ABC is minimum, is Ex (D) none or- 1 p 1 [S A0(1 0)+p(p (p3 -p+1) Hence A=-1p3-p+11 Now, minimum value of modulus is zero. Since A (p) is a cubic it must vanish for some p other than given as A, B,C - (D)] SUCCESS IN EE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) A graph is defined in polar co-ordinates as r(0)-cos +-. The smallest x-coordinates of any point on the graph is Ex. 16 4 [Sol. x-coordinate r cos (cos +-) cos cos 416 Hence smallest is - Ans. 16 SUCCESS IN EE MAIN 2019 ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) What is the y-intercept of the line that is parallel to y 3x, and which bisects the area of a rectangle with corners at (0, 0), (4, 0), (4, 2) and (0, 2)? Ex [Sol. Area of OADE = Area of ABCD since Area of ADD' Area of 'DA so area of rectangle AA'OE Area of rectangle D'DCB 4-h,-h y-3x+b (h22) 2-0 H0,2 C(4,2) AD h, -h (0,0)A D' (4,0) 2 10 -4- (hl,0) (h2,0) from (1) and (2) 2h, Equation of line AD is y-0-3 | x put x-0, get y--5 (0,-5) Ans. ] SUCCESS IN EE MAIN 2019 ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Given - and ax by 1 are two variable lines, 'a' and 'b' being the parameters connected by the relation ab2 ab The locus of the point of intersection has the equation (A") x2 + y2 + xy-1-0 (C) x2 + y2 + xy + 1-0 Ex (B) x2 + y2-xy + 1-0 (D) x2 + y2- -1-0 [So et (h, k) be point of intersection then given a +b-ab ah kb1 multiply h2+k2+hk(0+4)-1 SUCCESS IN EE MAIN 2019 ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. A ray of light passing through the point A(1, 2) is reflected at a point B on the x - axis and then passes through (5, 3). Then the equation of AB is (A*) 5x + 4y 13 (C) 4x + 5y 14 (B) 5x - 4y-3 (D) 4x - 5y6 13 N (5, 3) Hint A(1, 2 (a, 0) SUCCESS IN EE MAIN 2019 ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) -0, where 2 + -2, If the lines x + y + 1-0 ; 4x + 3y + 4-0 and x + y are concurrent then (A) -1, --1 Ex. (B) -1,p- 1 [Sol. Lines are x+y+1-0; 4x +3y +4-0 and x + y+ 0, where 2+p2-2 4 3 4 0 SUCCESS IN JEE MAIN 2019 ER. VINEET LOOMBA (IIT RooRKEE)

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