JEECONCEPTSBOOSTER
PARABOLA
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CONCEPTFORJEE||ChapterPARABOLA
1.STANDARDEQUATIONOFPARABOLA
1.Conicsectionintroduction
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CONCEPTFORJEE||ChapterPARABOLA
1.STANDARDEQUATIONOFPARABOLA
2.Conditiontorepresentpairoflinescircleandconic
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CONCEPTFORJEE||ChapterPARABOLA
1.STANDARDEQUATIONOFPARABOLA
3.Analyticaldefinitionofparabola
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CONCEPTFORJEE||ChapterPARABOLA
1.STANDARDEQUATIONOFPARABOLA
4.Equationofparabolainitsstandardform
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CONCEPTFORJEE||ChapterPARABOLA
1.STANDARDEQUATIONOFPARABOLA
5.Variousresultsofstandardequationofparabola
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CONCEPTFORJEE||ChapterPARABOLA
1.STANDARDEQUATIONOFPARABOLA
6.Tabularrepresentationofallstandardformsofparabolas
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CONCEPTFORJEE||ChapterPARABOLA
1.STANDARDEQUATIONOFPARABOLA
7.Parabolawithaxisparalleltocoordinateaxis
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CONCEPTFORJEE||ChapterPARABOLA
1.STANDARDEQUATIONOFPARABOLA
8.Positionofpointwithrespecttoparabolay2 = 4ax
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CONCEPTFORJEE||ChapterPARABOLA
1.STANDARDEQUATIONOFPARABOLA
9.Paraboliccurve
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CONCEPTFORJEE||ChapterPARABOLA
2.PROPERTIESOFFOCALCHORD
1.WhatisfocalChordandIfthechordjoiningP a t12; 2at1 andQ at22; 2at2 isthe
focalchord;thent1t2 = - 1
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CONCEPTFORJEE||ChapterPARABOLA
2.PROPERTIESOFFOCALCHORD
2.IfpointPis at2; 2at thenthelengthofthechordPQisa t +1t
2
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CONCEPTFORJEE||ChapterPARABOLA
2.PROPERTIESOFFOCALCHORD
3.Thelengthofthefocalchordwhichmakesanangleθwiththepositivedirectionofx-axisis4acosec2θ
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( ( ) ) ( )
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CONCEPTFORJEE||ChapterPARABOLA
2.PROPERTIESOFFOCALCHORD
4. Semi-latus rectum is the harmonicmean of SP andSQwhereP andQ are theextrimitiesofthefocalchord
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CONCEPTFORJEE||ChapterPARABOLA
2.PROPERTIESOFFOCALCHORD
5.Circledescribedonthefocallengthasdiametertouchesthetangentatthevertex
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CONCEPTFORJEE||ChapterPARABOLA
2.PROPERTIESOFFOCALCHORD
6.Circledescribedonthefocalchordasdiametertouchesthedirectrix.
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CONCEPTFORJEE||ChapterPARABOLA
3.INTERSECTIONOFALINEANDAPARABOLA
1.Intersectionofalineandaparabola
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CONCEPTFORJEE||ChapterPARABOLA
3.INTERSECTIONOFALINEANDAPARABOLA
2.Equationoftangenttoparabolay2 = 4ax
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CONCEPTFORJEE||ChapterPARABOLA
4.EQUATIONOFTANGENT
1.Equationoftangenttoparabolax2 = 4ay
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CONCEPTFORJEE||ChapterPARABOLA
4.EQUATIONOFTANGENT
2.Conditionforwhichy2 = 4axandx2 = 4byhavecommontangent
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CONCEPTFORJEE||ChapterPARABOLA
4.EQUATIONOFTANGENT
3.Findtheshortestdistancebetweentheliney = x - 2andtheparabolay = x2 + 3x + 2
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CONCEPTFORJEE||ChapterPARABOLA
4.EQUATIONOFTANGENT
4.PointofintersectionoftangentatanyTwopointsontheParabola
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CONCEPTFORJEE||ChapterPARABOLA
4.EQUATIONOFTANGENT
225.Locusoffootofperpendicularfromfocusuponanytangentistangentatvertex
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CONCEPTFORJEE||ChapterPARABOLA
4.EQUATIONOFTANGENT
6. Tangents at the end of focal chord are perpendicular to each other andmeet atdirectrix
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CONCEPTFORJEE||ChapterPARABOLA
4.EQUATIONOFTANGENT
7.Findthelocusofpointofintersectionoftangenttotheparabolay2 = 4axwhichareinclinedatanangleθtoeachother.
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CONCEPTFORJEE||ChapterPARABOLA
5.APPLICATIONSOFPARABOLA
1.Anarchisintheformofaparabolawithitsaxisvertical.Thearchis10mhighand5mwideatthebase.Howwideisit2mfromthevertexoftheparabola.
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CONCEPTFORJEE||ChapterPARABOLA
6.EQUATIONOFNORMAL
1.Equationofnormalat x1, y1 inParametricformslopeform
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( )
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CONCEPTFORJEE||ChapterPARABOLA
6.EQUATIONOFNORMAL
2.Equationofnormalforall4standardparabolas
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CONCEPTFORJEE||ChapterPARABOLA
7.PROPERTIESOFNORMAL
1.Normalotherthanaxisofparabolaneverpassesfromthefocus
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CONCEPTFORJEE||ChapterPARABOLA
7.PROPERTIESOFNORMAL
2.PointofintersectionofnormalatP at21, 2at1 andQ at22, 2at2
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CONCEPTFORJEE||ChapterPARABOLA
7.PROPERTIESOFNORMAL
3.NormalatP at21, 2at1 meetsthecurveagainatpointQ at22, 2at2 thent2 = - t1 -2t1
( ) ( )
( ) ( )
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CONCEPTFORJEE||ChapterPARABOLA
7.PROPERTIESOFNORMAL
4.LocusofPointofintersectionoftwonormalofparabolawhichareatrightangletooneother.
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CONCEPTFORJEE||ChapterPARABOLA
8.CO-NORMALPOINTS
1.Co-normalPoints
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CONCEPTFORJEE||ChapterPARABOLA
8.CO-NORMALPOINTS
2.Thealgebraicsumoftheordinatesofthefeetof3normalsdrawntotheparabolay2 = 4axfromagivenpointis0.
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CONCEPTFORJEE||ChapterPARABOLA
8.CO-NORMALPOINTS
3.CirclethroughConormalpoints
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CONCEPTFORJEE||ChapterPARABOLA
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8.CO-NORMALPOINTS
4. The centroid of the triangle formedby the feet of three normals to the parabolay2 = 4ax
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CONCEPTFORJEE||ChapterPARABOLA
8.CO-NORMALPOINTS
5. If threenormalsdrawn toanyparabola y2 = 4ax fromagivenpoint (h, k) are realthenh > 2a
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CONCEPTFORJEE||ChapterPARABOLA
9.REFLECTIONPROPERTYOFAPARABOLA
1.StateReflectionpropertyofparabola
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CONCEPTFORJEE||ChapterPARABOLA
10.CHORDOFCONTACT
1.ChordofContact
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CONCEPTFORJEE||ChapterPARABOLA
10.CHORDOFCONTACT
2.Equationofchordwhosemidpointis x1, y1( )
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CONCEPTFORJEE||ChapterPARABOLA
10.CHORDOFCONTACT
3.Findthelocusofmidpointnormalchordoftheparabolay2 = 4ax
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CONCEPTFORJEE||ChapterPARABOLA
10.CHORDOFCONTACT
4.Lettherebetwoparabolasy2 = 4axandy2 = - 4bx(wherea ≠ b; a; b > 0).Thenfindthe locusof themiddlepointsof the interceptsbetween theparabolasmadeon thelinesparalleltothecommonaxis.
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CONCEPTFORJEE||ChapterPARABOLA
11.POLEANDPOLAR
1.Definitionandmeaningofpoleandpolar
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CONCEPTFORJEE||ChapterPARABOLA
11.POLEANDPOLAR
2.Threenormalsaredrawnfromthepoint(c, 0)tothecurvey2 = x.Showthatcmust
begreaterthan12.Onenormalisalwaysthex-axis.Forwhatvaluesofcaretheother
twonormalsperpendiculartoeachother
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CONCEPTFORJEE||ChapterPARABOLA
12.INTERSECTIONWITHOTHERCONICS
1.IntersectionofParabolawithCircle
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CONCEPTFORJEE||ChapterPARABOLA
12.INTERSECTIONWITHOTHERCONICS
2.IntersectionofParabolawithellipse
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CONCEPTFORJEE||ChapterPARABOLA
12.INTERSECTIONWITHOTHERCONICS
3.IntersectionofParabolawithParabola
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CONCEPTFORJEE||ChapterPARABOLA
12.INTERSECTIONWITHOTHERCONICS
4.IntersectionofParabolawithHyperbola
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CONCEPTFORJEE||ChapterPARABOLA
12.INTERSECTIONWITHOTHERCONICS
5.Findthepointofintersectionofparabolay = - 3x2 + 3andhyperbolay = -18x
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