Question

if the circle x2+y2-2x+4y+1=0 complete one revolution on the positive direction of X axis then the centre in new position is​

Answer 1

Given :   circle x²+y²-2x+4y+1=0  complete one revolution on the positive direction of X axis

To Find :   the center in new position is​

Solution:

x²+y²-2x+4y+1=0

=> (x - 1)²  - 1 + ( y + 2)² - 4   + 1  =  0

=> (x - 1)² + ( y + 2)² = 2²

Center = ( 1 , - 2)

Radius =  2

After one complete revolution

Center will be shifted by 2πr  =  4π   as r = 2

Hence center =  ( 1 +  4π , - 2)

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