## Vineet Loomba is teaching live on Unacademy Plus

IIT-JEE CRASH COURSE FOR SURE SHOT SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Search vineet loomba unacademy" on GOOGLE IIT-JEE MATHS REVISION COURSE PREPARED BY: ER. VINEET LOOMBA IITian | IIT-JEE MENtOR

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B.Tech. From IIT Roorkee IIT-JEE Mentor Since 2010. Doubts/Feedback/Ideas 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 !!

PARABOLA (CRASH COURSE) FOR SURE SHOT SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) #CONIC SECTION (IMPORTANT POINTS) IIT-JEE MATHS REVISION COURSE PREPARED BY: ER. VINEET LOOMBA IITiAN | IIT-JEE MENTOR

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Topics Covered in this Video: OIntroduction to Conic Section O Identifying Conic Section through .Angle of intersecting plane .Eccentricity . Second degree equation O Finding Center of any Central Conic O Solved Examples MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Conic Sections Depending on the orientation of the intersecting plane, different types of conic sections will be generated from the double cone MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Identifying Conic Sections parabola circle hyperbola ellipse ...- MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Conic Section - Definitiorn P(h, k) A conic section or conic is the locus of a point P which moves in such a way that its distance from a fixed point S always bears a constant ratio to its distance from a fixed straight line, all being in the same plane. S( , ) SP -=constant = e (eccentricity) PM SP= e. PM e= 1 : Parabola e< 1 Ellipse e>1: Hyperbola e -0:Circle (special case ofellipse) Z' MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) y= sin(x) MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Case (i) When the focus lies on the directrix: In this case = abc + 2fgh-af2-bg2-cha_ 0 Condition 0 and h2 = ab = 0 and h> ab Shape A pair ofcoincident straight lines A pair ofreal straight lines A pair ofImaginary straight line 0 and h2 < ab MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Case (ii) When the focus does not lie on the directrix: Condition Shape a circle a parabola an Ellipse a Hyperbola a rectangular hyperbola #0,h=0, a = b 0, h2 > ab and a + b=0 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Solved Example The equation of the conic with focus at (1, -1), directrix along x-y+1-0 and with eccentricity 2 is (a) x2-y2=1 (c) 2xy 4x +4y +1-0 (d 2xy +4x -4y -1 0 (b) xy=1 (c) Let P (x, y) be any point on the conic. Then (x-1), (v +1)2 = J2| x-y +1). [Using SP = e.PM] V2 2xy-4x+4y + 1 = 0. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Solved Example The centre of 14x2 -4xy 11y2 - 44x - 58y +71 0 is os ox as oy = 0 28x-4y-44 = 0 = 0 4x + 22y-58 = 0 Solving these two equations we get (2,3) MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)