NARAYANA IIT ACADEMY,CP3, Indra Vihar, Talwandi, KOTA324005 Rajasthan, Ph.No.: 07443200119, Website : www.narayanaiitkota.com

Circle 38

CIRCLES1. LetL

1beastraightlinethroughtheoriginandL

2bethestraightlinex+y=1.Iftheintercepts

madebythecirclex2+y2x+3y=0onL1&L

2areequal,thenwhichofthefollowingequations

canrepresentL1?

(A)x+y=0 (B)xy=0 (C)x+7y=0 (D)x7y=0

2. The angle between a pair o f tangents drawn from a point P to the circle2 2 2 2x y 4x 6y 9sin 13cos 0 + + - + a + a = is2a .TheequationofthelocusofthepointPis

(A) 046422 = + - + + yxyx (B) 096422 = - - + + yxyx

(C) 046422 = - - + + yxyx (D) 096422 = + - + + yxyx

3. Iftwodistinctchords,drawnfromthepoint(p,q)onthecircle qypxyx + = + 22 (where qpq )arebisectedbythexaxis,then:(A)p2=q2 (B)p2=8q2 (C)p28q2

4. EquationofacircleS(x,y)=0,(S(2,3)=16)whichtouchestheline3x+4y7=0at(1,1)isgivenby(A)x2+y2+x+2y5=0 (B)x2+y2+2x+2y6=0(C)x2+y2+4x6y=0 (D)noneofthese

5. Thelengthoftheshortestchordofthecirclesx2+y2+2gx+2fy+c=0whichpassesthroughthepoint(a,b)insidethecircleis(A)2(a2+b2+2ga+2fb+c)1/2 (B)2[(a2+b2+2ga+2fb+c)]1/2

(C)[2(a2+b2+2ga+2fb+c)]1/2 (D)noneofthese

6. ApointPmovesinsuchawaythatPAPB

= l,where l ( , )0 1 isaconstantandA,Barefixed

pointssuchthatAB=a.LocusofPisacirclewhosediameterisequalto

(A)al

l1 2 -(B)

al l21 2( ) - (C)

21 2al l -

(D)noneofthese

7. AcirclepassesthroughthepointsA(1,0),B(5,0)andC(0,h).If ACB ismaximumthen

(A)h= 5 (B)h= 2 5 (C)h= 10 (D)h= 2 10

8. Acircletouchestheliney=xatapointPsuchthatOP= 24 whereOisorigin.Thecirclecontainsthepoint(10,2)initsinterior&thelengthofitschordontheline,x+y=0is

26 .Determinetheequationofthecircle.

9. LetCbeanycirclewithcentre ( )20, .ProvethatatthemosttworationalpointscanbethereonC(Arationalpointisapointbothofwhosecoordinatearerationalnumbers).

10. Foreachnaturalnumberk,letCkdenotethecirclewithradiuskcentrimeteresandcentreatthe

origin.OnthecircleCk, aparticlemoveskcentrimeteresinthecounterclockwisedirection.

AftercompletingitsmotiononCk,theparticlemovestoC

k+1intheradialdirection.Themotionof

theparticlecontinuesinthismanner.Theparticlestartsat(1,0).IftheparticlecorssesthepositivedirectionofthexaxisforthefirsttimeonthecircleC

nthenn=................

NARAYANA IIT ACADEMY,CP3, Indra Vihar, Talwandi, KOTA324005 Rajasthan, Ph.No.: 07443200119, Website : www.narayanaiitkota.com

Circle 39

ANSWERKEY1. BC 2. B 3. D 4. A

5. B 6. C 7. A

8. x2+y2+18x2y+32=0 10. 7