ELLIPSE. 1. If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is [Karnataka CET 2000]

Similar documents

[Q. Booklet Number]

Time: 2 hours IIT-JEE 2006-MA-1. Section A (Single Option Correct) + is (A) 0 (B) 1 (C) 1 (D) 2. lim (sin x) + x 0. = 1 (using L Hospital s rule).

Lesson-5 ELLIPSE 2 1 = 0

Inverse Trigonometrical Functions 1. Properties of Inverse Trigonometrical Function. 1. The domain of sin x is [Roorkee Screening 1993] (a) (d)

UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION. (2014 Admn. onwards) III Semester. B.Sc. Mathematics CORE COURSE CALCULUS AND ANALYTICAL GEOMETRY


/ 3, then (A) 3(a 2 m 2 + b 2 ) = 4c 2 (B) 3(a 2 + b 2 m 2 ) = 4c 2 (C) a 2 m 2 + b 2 = 4c 2 (D) a 2 + b 2 m 2 = 4c 2

, MATHS H.O.D.: SUHAG R.KARIYA, BHOPAL, CONIC SECTION PART 8 OF

PhysicsAndMathsTutor.com

Drill Exercise Find the coordinates of the vertices, foci, eccentricity and the equations of the directrix of the hyperbola 4x 2 25y 2 = 100.

Name of the Student:

Ellipse. 1. Defini t ions. FREE Download Study Package from website: 11 of 91CONIC SECTION

CONIC SECTIONS. Chapter 11

VITEEE 2018 MATHEMATICS QUESTION BANK

HYPERBOLA. AIEEE Syllabus. Total No. of questions in Ellipse are: Solved examples Level # Level # Level # 3..

NORMALS. a y a y. Therefore, the slope of the normal is. a y1. b x1. b x. a b. x y a b. x y

Mathematics Extension 2

Mathematics Extension 2

Linford 1. Kyle Linford. Math 211. Honors Project. Theorems to Analyze: Theorem 2.4 The Limit of a Function Involving a Radical (A4)

HIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 3 UNIT (ADDITIONAL) AND 3/4 UNIT (COMMON) Time allowed Two hours (Plus 5 minutes reading time)

HIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 4 UNIT (ADDITIONAL) Time allowed Three hours (Plus 5 minutes reading time)

E R K HSS ERUMIYAMPATTI Page 1 +2 STUDY MATERIALS

Add Maths Formulae List: Form 4 (Update 18/9/08)

Mathematics Last Minutes Review

P 1 (x 1, y 1 ) is given by,.

National Quali cations AHEXEMPLAR PAPER ONLY

Set 1 Paper 2. 1 Pearson Education Asia Limited 2014

ELLIPSE. Standard equation of an ellipse referred to its principal axes along the co-ordinate axes is. ( a,0) A'

JEE(Advanced) 2018 TEST PAPER WITH SOLUTION (HELD ON SUNDAY 20 th MAY, 2018)


Objective Mathematics

BC Calculus Review Sheet

Set 3 Paper 2. Set 3 Paper 2. 1 Pearson Education Asia Limited 2017

For all Engineering Entrance Examinations held across India. Mathematics

Mathematics Extension 2

(1) Functions A relationship between two variables that assigns to each element in the domain exactly one element in the range.

334 MATHS SERIES DSE MATHS PREVIEW VERSION B SAMPLE TEST & FULL SOLUTION

PhysicsAndMathsTutor.com

[BIT Ranchi 1992] (a) 2 (b) 3 (c) 4 (d) 5. (d) None of these. then the direction cosine of AB along y-axis is [MNR 1989]

Graphing Review Part 3: Polynomials

WBJEE Answer Keys by Aakash Institute, Kolkata Centre

GRADE 12 SEPTEMBER 2016 MATHEMATICS P1

PEPERIKSAAN PERCUBAAN SPM TAHUN 2007 ADDITIONAL MATHEMATICS. Form Five. Paper 2. Two hours and thirty minutes

Sketch graphs of conic sections and write equations related to conic sections

Algebra II Notes Unit Ten: Conic Sections

Force and Motion. Force

Name: A2RCC Midterm Review Unit 1: Functions and Relations Know your parent functions!

ASSERTION AND REASON

Log1 Contest Round 1 Theta Equations & Inequalities. 4 points each. 5 points each. 7, a c d. 9, find the value of the product abcd.

EXERCISE a a a 5. + a 15 NEETIIT.COM

Mathematics for Engineers Part II (ISE) Version 1.1/

02 - COMPLEX NUMBERS Page 1 ( Answers at the end of all questions ) l w l = 1, then z lies on

Qn Suggested Solution Marking Scheme 1 y. G1 Shape with at least 2 [2]

GRAPHING LINEAR EQUATIONS. Linear Equations. x l ( 3,1 ) _x-axis. Origin ( 0, 0 ) Slope = change in y change in x. Equation for l 1.

(200 terms) equals Let f (x) = 1 + x + x 2 + +x 100 = x101 1

Objective Mathematics

Theorem 5.3 (Continued) The Fundamental Theorem of Calculus, Part 2: ab,, then. f x dx F x F b F a. a a. f x dx= f x x

FP3 past questions - conics

SLIP TEST 3 Chapter 2,3 and 6. Part A Answer all the questions Each question carries 1 mark 1 x 1 =1.

8.6 The Hyperbola. and F 2. is a constant. P F 2. P =k The two fixed points, F 1. , are called the foci of the hyperbola. The line segments F 1

Synopsis Grade 12 Math Part II


MODEL SOLUTIONS TO IIT JEE 2009

For students entering Honors Precalculus Summer Packet

Objective Mathematics

3 Show in each case that there is a root of the given equation in the given interval. a x 3 = 12 4

MATHEMATICS PAPER IIB COORDINATE GEOMETRY AND CALCULUS. Note: This question paper consists of three sections A,B and C. SECTION A

( ) D) E) NOTA

Force and Motion. Force. Classifying Forces. Physics 11- Summer /21/01. Chapter 4 material 1. Forces are vector quantities!

Math 122 Test 3 - Review 1

MAHESH TUTORIALS SUBJECT : Maths(012) First Preliminary Exam Model Answer Paper

Important Facts You Need To Know/Review:

Mathematics Extension 2

Assignment ( ) Class-XI. = iii. v. A B= A B '

Mathematics. Area under Curve.

1. If y 2 2x 2y + 5 = 0 is (A) a circle with centre (1, 1) (B) a parabola with vertex (1, 2) 9 (A) 0, (B) 4, (C) (4, 4) (D) a (C) c = am m.

A quick overview of the four conic sections in rectangular coordinates is presented below.

k ) and directrix x = h p is A focal chord is a line segment which passes through the focus of a parabola and has endpoints on the parabola.

KEY CONCEPTS. satisfies the differential equation da. = 0. Note : If F (x) is any integral of f (x) then, x a

1 is equal to. 1 (B) a. (C) a (B) (D) 4. (C) P lies inside both C & E (D) P lies inside C but outside E. (B) 1 (D) 1

UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION

1. If * is the operation defined by a*b = a b for a, b N, then (2 * 3) * 2 is equal to (A) 81 (B) 512 (C) 216 (D) 64 (E) 243 ANSWER : D

Things I Should Know In Calculus Class

Interpolation. 1. What is interpolation?

Chapter 30: Reflection and Refraction

CALCULUS BASIC SUMMER REVIEW

Mathematics [Summary]

Time : 3 hours 03 - Mathematics - March 2007 Marks : 100 Pg - 1 S E CT I O N - A

National Quali cations SPECIMEN ONLY

PhysicsAndMathsTutor.com

Draft. Complex numbers. Orientation

CONVERGENCE OF THE RATIO OF PERIMETER OF A REGULAR POLYGON TO THE LENGTH OF ITS LONGEST DIAGONAL AS THE NUMBER OF SIDES OF POLYGON APPROACHES TO


F x = 2x λy 2 z 3 = 0 (1) F y = 2y λ2xyz 3 = 0 (2) F z = 2z λ3xy 2 z 2 = 0 (3) F λ = (xy 2 z 3 2) = 0. (4) 2z 3xy 2 z 2. 2x y 2 z 3 = 2y 2xyz 3 = ) 2

Vectors. Vectors in Plane ( 2

CET MOCK TEST If a,b,c are p, q and r terms repectively of a G.P., then (q-r)loga+(r-p)logb+(p-q)logc= a)0 b) 1 c)-1 d)abc

Solutions to Problem Set 7

Students must always use correct mathematical notation, not calculator notation. the set of positive integers and zero, {0,1, 2, 3,...

by Abhijit Kumar Jha

Transcription:

ELLIPSE. If the ltus rectum of ellipse e equl to hlf of its mior is, the its eccetricit is [Krtk CET 000] / / / d /. The legth of the ltus rectum of the ellipse is [MNR 7, 0, ] / / / d 0/. Eccetricit of the coic 6 7 is [MNR ] / 7 7/6 / d /. The legths of mjor d mior is of ellipse re 0 d respectivel d its mjor is log the -is. The equtio of the ellipse referred to its cetre s origi is [P. CET 00] 6 6 d 00 6 6 00. If the cetre, oe of the foci d semi-mjor is of ellipse e 0, 0, 0, d the its equtio is [AMU ] 6 6 6. The equtio 0 represets [MP PET ] A circle A ellipse A hperol d A prol 7. The equtio of the ellipse whose ltus rectum is d whose eccetricit is, referred to the pricipl es of coordites, is [MP PET ] d 6 6. For the ellipse, the legth of ltus rectum is [MNR 7] d. For the ellipse, the eccetricit is [MNR 7] 6 7 d

0. If the legth of the mjor is of ellipse is three times the legth of its mior is, the its eccetricit is [EAMCET 0] d. The legth of the ltus rectum of ellipse is of the mjor is. Its eccetricit is 7 d [EAMCET ]. A ellipse is descried usig edless strig which is pssed over two pis. If the es re 6 cm d cm, the ecessr legth of the strig d the distce etwee the pis respectivel i cm, re [MNR ] 6, 6,, r r. The equtio 0 represets ellipse, if [MP PET ] r r r. The locus of the poit of itersectio of perpediculr tgets to the ellipse, is d [MP PET ]. The legth of the ltus rectum of the ellipse [Krtk CET ] 6 /6 7/7 7/ d / 6. The equtio of the ellipse whose oe focus is t, 0 d whose eccetricit is /, is [Krtk CET ] d 7. The foci of 6 00 re [BIT Rchi 6], 0 0,, d,. Eccetricit of the ellipse is [Kerl Egg. 00] d

. The legth of the ltus rectum of the ellipse, is [MP PET ] d 0. The locus of vrile poit whose distce from, 0 is times its distce from the lie, is [IIT ] Ellipse Prol Hperol. If P,,, 0 F, 0 d 6 00, the PF PF equls [IIT ] 6 0 d. P is poit o the ellipse 6, whose foci re S d S. The SP S' P equls [DCE ] 6 d. Wht is the equtio of the ellipse with foci, 0 d eccetricit 0 d 0 [DCE ]. The eccetricit of the ellipse 6, is [MP PET 000] d 6. The eccetricit of the ellipse 6 00 is [MP PET 00] / / / d / 6. The distce etwee the foci of ellipse is 6 d eccetricit is. Legth of the mjor is of the ellipse is [Krtk CET 00] 6 6 d 7. If the eccetricit of the two ellipse d re equl, the the vlue of 6 is [UPSEAT 00] / 6/ / d /6. I the ellipse, mior is is d eccetricit is. The mjor is is [Krtk CET 00] 6 0 d 6. I ellipse, the distce etwee the foci is [Krtk CET 00] /

d 0. Equtio of the ellipse with eccetricit d foci t, 0 is [MP PET 00]. The sum of focl distces of poit o the ellipse with mjor d mior es s d respectivel, is equl to [MP PET 00] d. I ellipse the distce etwee its foci is 6 d its mior is is. The its eccetricit is [EAMCET ] d. If r of give legth moves with its etremities o two fied stright lies t right gles, the the locus of poit o r mrked o the r descries / [Oriss JEE 00] Circle Prol Ellipse d Hperol. The cetre of the ellipse 6 6 0 is [MP PET ],,, d,. Ltus rectum of ellipse 6 0 is [MP PET ] / / d 6/ 6. The equtio 7 0 represets [BIT Rchi 6] A circle A ellipse A hperol d A rectgulr hperol 6 7. The cetre of the ellipse is [EAMCET ] 0, 0,, 0 d 0,. The equtio of ellipse whose focus,, whose directri is 0 d whose eccetricit is, is give [MP PET ] 7 7 0 0 7 0 7 7 0 0 7 0 7 7 0 0 7 0 d 7 7 0 0 7 0. The foci of the ellipse re t [MNR ; MP PET ;], d, 6, d 6,

, d, 6 d, d, 6 0. The eccetricit of the ellipse 0 0, is [MNR ; P. CET 00] / / /. The curve represeted cos t sit, cos t sit is [EAMCET ; DCE 000] Ellipse Prol Hperol d Circle. The eccetricit of the ellipse 6 0 is [MP PET 6] 6 d. The eccetricit of the curve represeted the equtio 0 is [Roorkee ] 0 / / d. For the ellipse 0 0 0 the eccetricit e [Krtk CET 00] / / / d /. The eccetricit of the ellipse is [AMU ] / / / d Imgir 6. The legth of the es of the coic 6 0, re [Oriss JEE 00],,, d, 7. The eccetricit of the ellipse 6 0 is [EAMCET 00] / / / d /. The eccetricit of the coic 6 is [MP PET 00] d. If the lie c e tget to the ellipse 6 d, the c [MNR 7; DCE 000] 0. The positio of the poit, with respect to the ellipse 6 6 0 [MP PET ] Outside the ellipse O the ellipse O the mjor is d O the mior is

. The gle etwee the pir of tgets drw to the ellipse from the poit,, is [MNR ] t t 6 t d t. The equtios of the tgets of the ellipse 6 which psses through the poit, is [MP PET 6],,, d,. If the lie m c touches the ellipse m m m d m. The ellipse d the stright lie m c m c m c d c, the c [MNR 7; MP PET ] m c itersect i rel poits ol if [MNR ]. The locus of the poit of itersectio of the perpediculr tgets to the ellipse is d [Krtk CET 00] 6. Eccetric gle of poit o the ellipse 6 t distce uits from the cetre of the ellipse is [WB JEE 0] d, 7. The equtio of the tgets drw t the eds of the mjor is of the ellipse 0 0 re [MP PET ] 0, 6. The equtio of orml t the poit 0, of the ellipse is [MP PET ] 0 0 -is d -is. The equtio of the orml t the poit, o the ellipse 6 0, is [MP PET 000] 0 7 0 7 0 d 7 0 60. If the lie cos si p e orml to the ellipse, the [MP PET 00] p cos si p cos si p sec cosec

d cosec sec p 6. The lie 0 m l is orml to the ellipse, if [DCE 000] l m m l m l