CBSE Class 12-science Answered

Let the equation of circle be

The circle given by eqn.(1) passes through origin (0,0)

Hence c = 0 .

The circle given by eqn.(1) passes through origin (1,0)

Hence we get,  2 g + 1 = 0   or  g = -1/2

Hence , center C of circle is ( 1/2 , -f )

Circle given by eqn.(1) touches the circle " x² + y² = 9 " ( Orange colour circle in figure )

Let the circles touch at point P as shown in figure. Let C be the center of circle that is to be determined.

Points O , C and P are in line

Hence , as shown from figure ,

OC = OP - PC

By solving above expression , we get f = ±√2

Hence centre of circle (-g, -f ) is   either ( 1/2 , +√2 )   or ( 1/2 , - √2 )

Answer :-

option (d) ( 1/2 , - √2 )