+91-93193 64476
FlagBACK
Flag Analytical Geometry> straight-lines...
question mark

A particle begins at the origin and moves successively, 1 unit to the right, 1/2 unit up, 1/4 unit to the left, 1/8 unit down, 1/16 unit to the right, 1/32 unit up etc.The length of each move is half the length of previous move and movement continues indefinitely.The co-ordinates of the point to which the movement converges is :

chaman , 12 Years ago
Grade 12
anser 2 Answers
Saurabh Singh
x coordinate = 1-(1/4)+(1/16)-(1/64).......
y coordinate = (1/2) -(1/8) + (1/32) .........

converge the above two series to get the X and Y as the result of converging coordinate

Thanks & Regards

Saurabh Singh,

askIITians Faculty

B.Tech.

IIT Kanpur

Last Activity: 12 Years ago
Ajay Verma
ans:

total displacement in X direction :
step-1 : 1 unit right (+ve X direction)
step-3 : 1/22unit left (-ve X deirction)
step-5: 1/24unit right ( +ve X direction)
step-7 : 1/26unit ( -ve X direction)
and so on..
so total displacement in X direction: (X-coordinate)
X= 1 - 1/22+ 1/24_1/26+ 1/28 - ........................................ up to infinity
its an G.P. so sum of it :
X = 1/ {1+ 1/22} sum of G.P = a/ (1-r)
1st term = 1 and C.R. = -1/22
X = 4/5


similarly
total displacement in Y direction :
step-2 : 1/2 unit up (+ve Y direction)
step-4 : 1/23unit down (-ve Y deirction)
step-6: 1/25unit up ( +ve Y direction)
step-7 : 1/27unit ( -ve Y direction)
and so on..
so total displacement in Y direction: (Y-coordinate):

Y= 1/2 - 1/23+ 1/25 - 1/27.................................................. up to infinity
its a g.p.
so sum : Y = 1/2*{1 +1/22} 1st term = 1/2 and C.R. = -1/22
Y = 2/5

so coordinates : (4/5 , 2/5)


Thanks and Regards,
Ajay verma,
askIITians faculty,
IIT HYDERABAD
Last Activity: 12 Years ago
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Other Related Questions on analytical geometry

question mark
  • The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is 
analytical geometry
1 Answer Available

Last Activity: 3 Years ago

question mark
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius. 
 
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
analytical geometry
1 Answer Available

Last Activity: 4 Years ago