## 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) #STANDARD AND SHIFTED PARABOLAS IIT-JEE MATHS REVISION COURSE PREPARED BY: ER. VINEET LOOMBA IITiAN | IIT-JEE MENTOR

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) PARABOLA For parabola y2 4ax: (i) Vertex is (0, 0) (ii) focus is (a, 0) (iii) Axis is y -0 (iv) Directrix is x +a-0 S (a,0) N axis Pr SP PM = 4ax MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) 2 = 4ax Focal Distance: The distance of a point on the parabola from the focus. IM Focal Chord: A chord of the parabola, which passes through the focus. Double Ordinate: A chord of the parabola perpendicular to the axis of the symmetry Latus Rectum: A double ordinate passing through the focus or a focal chord perpendicular to the axis of parabola is called the Latus Rectum (L.R.)(-4a). X S (a, 0 N axis L' = 4ax MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Eqaution of parabola -4ax x2 = 4ay x2--4ay CD Y Graph AL A S(a,0) S(-a, 0) Equation of the axis Vertex: Focus Equation of the Directrix Equation of Latus ractum Length of Latus ractum Tangent at the vertex (0,0) (a, 0) (0, 0) (0, a) (0, 0) (0, 0) x=a 4a MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Solved Example Find the equation of the parabola whose focus is at (1, 2) and the directrix the line x- 2y 3 0. Solution Let P(x, y) be any point on the parabola whose focus is S(- 1, 2) and the directrix x-2y + 3 = 0. Draw PM perpendicular to directrix x-2y + 3-0. Then by definition, SP PM P(x, y) 2 2 (1+1)2 + (y + 2)2 = 1+4 5 [(x + 1 )2 + (y + 2)2] = (x-2y + 3)? 5(x2 + y2 + 2x + 4y + 5) = (x2 + 4y2 +9-4xy + 6x-12y) This is the equation of the required parabola. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Find the coordinates of focus, vertex, equation of directrix, tangent at vertex, axis and length of latus of rectum for the parabola. y26x Solution: 3 Focus : (a, 0)--0 Vertex: (0, 0) Tangent at vertexx 0 Axis : y=0 Length of latus rectum = 4-6 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Example: The equation of the directrix of the parabola y +4y +4x +2-0 is [IT Screeningl a) X= (b) x=1 (c) x 2 Solution : (d) Here, y, 4y + 4 + 4x-2-0 or (y + 2)2 =-4 x 2 Let y+2-Y, x =X. Then the parabola is Y2-4X 2 3 2 The directrix is X+1-0or_-x+1=0,.:x= 2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) The line x-1 = 0 is the directrix of the parabola y 2- Then one of the values of k is Example: [IIT Screening] (b) 8 4 8 Solution : (c) The parabola is y2-4 |x- Putting y Y, x--X The equation is Y 2-4. .x The directrix is X +-= 0 i. e.. x--+-= 0 4 But x-1 = 0 is the directrix. So MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)