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Question

The center of a circle passing through the points 0,0,1,0 and touching the circle x2+y2=9 is


A

32,12

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B

12,32

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C

12,12

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D

12,-21/2

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Solution

The correct option is D

12,-21/2


Explanation for the correct option:

Finding the center of the circle:

The general equation of the circle is x2+y2+2gx+2fy+c=0 with center -g,-f and radius g2+f2-c

Circle passes through the point 0,0.

So, substitute x=0 and y=0 in x2+y2+2gx+2fy+c=0.

c=0

Similarly, Circle passes through the point 1,0.

So, substitute x=1 and y=0 in x2+y2+2gx+2fy=0

.

1+2g=0g=-1/2

Now the circle touches another circle with equation x2+y2=9.

Since the center of the this circle lies on the circle 1, the radius of a new circle is equal to the diameter of the circle 1.

2g2+f2-c=3142+f2=32122+f2=94f2=94-14=2f=±2

Hence the centres of circle 1 is -g,-f=12,±2 .

Therefore, the correct answer is option (D).


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