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JEE CONCEPTS BOOSTER PARABOLA Download Doubtnut Today Ques No. Question 1 CONCEPT FOR JEE || Chapter PARABOLA 1. STANDARD EQUATION OF PARABOLA 1. Conic section introduction Click to LEARN this concept/topic on Doubtnut 2 CONCEPT FOR JEE || Chapter PARABOLA 1. STANDARD EQUATION OF PARABOLA 2. Condition to represent pair of lines circle and conic Click to LEARN this concept/topic on Doubtnut 3 CONCEPT FOR JEE || Chapter PARABOLA 1. STANDARD EQUATION OF PARABOLA 3. Analytical definition of parabola Click to LEARN this concept/topic on Doubtnut

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Page 1: Click to LEARN this concept/topic on Doubtnut...CONCEPT FOR JEE || Chapter PARABOLA 8. CO-NORMAL POINTS 2. The algebraic sum of the ordinates of the feet of 3 normals drawn to the

JEECONCEPTSBOOSTER

PARABOLA

DownloadDoubtnutToday

QuesNo. Question

1

CONCEPTFORJEE||ChapterPARABOLA

1.STANDARDEQUATIONOFPARABOLA

1.Conicsectionintroduction

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2

CONCEPTFORJEE||ChapterPARABOLA

1.STANDARDEQUATIONOFPARABOLA

2.Conditiontorepresentpairoflinescircleandconic

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3

CONCEPTFORJEE||ChapterPARABOLA

1.STANDARDEQUATIONOFPARABOLA

3.Analyticaldefinitionofparabola

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Page 2: Click to LEARN this concept/topic on Doubtnut...CONCEPT FOR JEE || Chapter PARABOLA 8. CO-NORMAL POINTS 2. The algebraic sum of the ordinates of the feet of 3 normals drawn to the

4

CONCEPTFORJEE||ChapterPARABOLA

1.STANDARDEQUATIONOFPARABOLA

4.Equationofparabolainitsstandardform

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5

CONCEPTFORJEE||ChapterPARABOLA

1.STANDARDEQUATIONOFPARABOLA

5.Variousresultsofstandardequationofparabola

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6

CONCEPTFORJEE||ChapterPARABOLA

1.STANDARDEQUATIONOFPARABOLA

6.Tabularrepresentationofallstandardformsofparabolas

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7

CONCEPTFORJEE||ChapterPARABOLA

1.STANDARDEQUATIONOFPARABOLA

7.Parabolawithaxisparalleltocoordinateaxis

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8

CONCEPTFORJEE||ChapterPARABOLA

1.STANDARDEQUATIONOFPARABOLA

8.Positionofpointwithrespecttoparabolay2 = 4ax

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Page 3: Click to LEARN this concept/topic on Doubtnut...CONCEPT FOR JEE || Chapter PARABOLA 8. CO-NORMAL POINTS 2. The algebraic sum of the ordinates of the feet of 3 normals drawn to the

9

CONCEPTFORJEE||ChapterPARABOLA

1.STANDARDEQUATIONOFPARABOLA

9.Paraboliccurve

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10

CONCEPTFORJEE||ChapterPARABOLA

2.PROPERTIESOFFOCALCHORD

1.WhatisfocalChordandIfthechordjoiningP a t12; 2at1 andQ at22; 2at2 isthe

focalchord;thent1t2 = - 1

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11

CONCEPTFORJEE||ChapterPARABOLA

2.PROPERTIESOFFOCALCHORD

2.IfpointPis at2; 2at thenthelengthofthechordPQisa t +1t

2

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12

CONCEPTFORJEE||ChapterPARABOLA

2.PROPERTIESOFFOCALCHORD

3.Thelengthofthefocalchordwhichmakesanangleθwiththepositivedirectionofx-axisis4acosec2θ

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( ( ) ) ( )

( ) ( )

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Page 4: Click to LEARN this concept/topic on Doubtnut...CONCEPT FOR JEE || Chapter PARABOLA 8. CO-NORMAL POINTS 2. The algebraic sum of the ordinates of the feet of 3 normals drawn to the

13

CONCEPTFORJEE||ChapterPARABOLA

2.PROPERTIESOFFOCALCHORD

4. Semi-latus rectum is the harmonicmean of SP andSQwhereP andQ are theextrimitiesofthefocalchord

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14

CONCEPTFORJEE||ChapterPARABOLA

2.PROPERTIESOFFOCALCHORD

5.Circledescribedonthefocallengthasdiametertouchesthetangentatthevertex

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15

CONCEPTFORJEE||ChapterPARABOLA

2.PROPERTIESOFFOCALCHORD

6.Circledescribedonthefocalchordasdiametertouchesthedirectrix.

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16

CONCEPTFORJEE||ChapterPARABOLA

3.INTERSECTIONOFALINEANDAPARABOLA

1.Intersectionofalineandaparabola

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17

CONCEPTFORJEE||ChapterPARABOLA

3.INTERSECTIONOFALINEANDAPARABOLA

2.Equationoftangenttoparabolay2 = 4ax

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18

CONCEPTFORJEE||ChapterPARABOLA

4.EQUATIONOFTANGENT

1.Equationoftangenttoparabolax2 = 4ay

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19

CONCEPTFORJEE||ChapterPARABOLA

4.EQUATIONOFTANGENT

2.Conditionforwhichy2 = 4axandx2 = 4byhavecommontangent

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20

CONCEPTFORJEE||ChapterPARABOLA

4.EQUATIONOFTANGENT

3.Findtheshortestdistancebetweentheliney = x - 2andtheparabolay = x2 + 3x + 2

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21

CONCEPTFORJEE||ChapterPARABOLA

4.EQUATIONOFTANGENT

4.PointofintersectionoftangentatanyTwopointsontheParabola

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CONCEPTFORJEE||ChapterPARABOLA

4.EQUATIONOFTANGENT

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Page 6: Click to LEARN this concept/topic on Doubtnut...CONCEPT FOR JEE || Chapter PARABOLA 8. CO-NORMAL POINTS 2. The algebraic sum of the ordinates of the feet of 3 normals drawn to the

225.Locusoffootofperpendicularfromfocusuponanytangentistangentatvertex

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23

CONCEPTFORJEE||ChapterPARABOLA

4.EQUATIONOFTANGENT

6. Tangents at the end of focal chord are perpendicular to each other andmeet atdirectrix

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24

CONCEPTFORJEE||ChapterPARABOLA

4.EQUATIONOFTANGENT

7.Findthelocusofpointofintersectionoftangenttotheparabolay2 = 4axwhichareinclinedatanangleθtoeachother.

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25

CONCEPTFORJEE||ChapterPARABOLA

5.APPLICATIONSOFPARABOLA

1.Anarchisintheformofaparabolawithitsaxisvertical.Thearchis10mhighand5mwideatthebase.Howwideisit2mfromthevertexoftheparabola.

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26

CONCEPTFORJEE||ChapterPARABOLA

6.EQUATIONOFNORMAL

1.Equationofnormalat x1, y1 inParametricformslopeform

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( )

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27

CONCEPTFORJEE||ChapterPARABOLA

6.EQUATIONOFNORMAL

2.Equationofnormalforall4standardparabolas

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28

CONCEPTFORJEE||ChapterPARABOLA

7.PROPERTIESOFNORMAL

1.Normalotherthanaxisofparabolaneverpassesfromthefocus

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29

CONCEPTFORJEE||ChapterPARABOLA

7.PROPERTIESOFNORMAL

2.PointofintersectionofnormalatP at21, 2at1 andQ at22, 2at2

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30

CONCEPTFORJEE||ChapterPARABOLA

7.PROPERTIESOFNORMAL

3.NormalatP at21, 2at1 meetsthecurveagainatpointQ at22, 2at2 thent2 = - t1 -2t1

( ) ( )

( ) ( )

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31

CONCEPTFORJEE||ChapterPARABOLA

7.PROPERTIESOFNORMAL

4.LocusofPointofintersectionoftwonormalofparabolawhichareatrightangletooneother.

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32

CONCEPTFORJEE||ChapterPARABOLA

8.CO-NORMALPOINTS

1.Co-normalPoints

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33

CONCEPTFORJEE||ChapterPARABOLA

8.CO-NORMALPOINTS

2.Thealgebraicsumoftheordinatesofthefeetof3normalsdrawntotheparabolay2 = 4axfromagivenpointis0.

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34

CONCEPTFORJEE||ChapterPARABOLA

8.CO-NORMALPOINTS

3.CirclethroughConormalpoints

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CONCEPTFORJEE||ChapterPARABOLA

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Page 9: Click to LEARN this concept/topic on Doubtnut...CONCEPT FOR JEE || Chapter PARABOLA 8. CO-NORMAL POINTS 2. The algebraic sum of the ordinates of the feet of 3 normals drawn to the

35

8.CO-NORMALPOINTS

4. The centroid of the triangle formedby the feet of three normals to the parabolay2 = 4ax

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36

CONCEPTFORJEE||ChapterPARABOLA

8.CO-NORMALPOINTS

5. If threenormalsdrawn toanyparabola y2 = 4ax fromagivenpoint (h, k) are realthenh > 2a

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37

CONCEPTFORJEE||ChapterPARABOLA

9.REFLECTIONPROPERTYOFAPARABOLA

1.StateReflectionpropertyofparabola

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38

CONCEPTFORJEE||ChapterPARABOLA

10.CHORDOFCONTACT

1.ChordofContact

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39

CONCEPTFORJEE||ChapterPARABOLA

10.CHORDOFCONTACT

2.Equationofchordwhosemidpointis x1, y1( )

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40

CONCEPTFORJEE||ChapterPARABOLA

10.CHORDOFCONTACT

3.Findthelocusofmidpointnormalchordoftheparabolay2 = 4ax

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41

CONCEPTFORJEE||ChapterPARABOLA

10.CHORDOFCONTACT

4.Lettherebetwoparabolasy2 = 4axandy2 = - 4bx(wherea ≠ b; a; b > 0).Thenfindthe locusof themiddlepointsof the interceptsbetween theparabolasmadeon thelinesparalleltothecommonaxis.

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42

CONCEPTFORJEE||ChapterPARABOLA

11.POLEANDPOLAR

1.Definitionandmeaningofpoleandpolar

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43

CONCEPTFORJEE||ChapterPARABOLA

11.POLEANDPOLAR

2.Threenormalsaredrawnfromthepoint(c, 0)tothecurvey2 = x.Showthatcmust

begreaterthan12.Onenormalisalwaysthex-axis.Forwhatvaluesofcaretheother

twonormalsperpendiculartoeachother

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44

CONCEPTFORJEE||ChapterPARABOLA

12.INTERSECTIONWITHOTHERCONICS

1.IntersectionofParabolawithCircle

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45

CONCEPTFORJEE||ChapterPARABOLA

12.INTERSECTIONWITHOTHERCONICS

2.IntersectionofParabolawithellipse

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46

CONCEPTFORJEE||ChapterPARABOLA

12.INTERSECTIONWITHOTHERCONICS

3.IntersectionofParabolawithParabola

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47

CONCEPTFORJEE||ChapterPARABOLA

12.INTERSECTIONWITHOTHERCONICS

4.IntersectionofParabolawithHyperbola

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48

CONCEPTFORJEE||ChapterPARABOLA

12.INTERSECTIONWITHOTHERCONICS

5.Findthepointofintersectionofparabolay = - 3x2 + 3andhyperbolay = -18x

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