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question 13
Asked by klmn445 | 03 Apr, 2024, 11:33: PM

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 )

option (d) ( 1/2 , - √2 )

Answered by Thiyagarajan K | 04 Apr, 2024, 10:45: AM

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