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Question

The equation of the image of circle x2+y22x4y=0 in the line 3x4y+30=0 is

A
(x5)2+(y10)2=5
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B
(x+5)2+(y+10)2=5
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C
(x+5)2+(y10)2=5
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D
(x5)2+(y+10)2=5
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Solution

The correct option is C (x+5)2+(y10)2=5
Given circle is x2+y22x4y=0
which is in the form of x2+y2+2gx+2fy+c=0.
Then g=1, f=2, c=0
The centre and radius of the circle is
C=(1,2)
and r=g2+f2c=1+40
r=5

Now, the image of the centre in the given line is
x13=y24=2(3×14×2+30)32+(4)2x=5, y=10

So, the centre of image circle is
C1=(5,10)
And radius is same as 5

Hence, the equation of image circle is
(x+5)2+(y10)2=5

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