The correct option is C (x+5)2+(y−10)2=5
Given circle is x2+y2−2x−4y=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+f2−c=√1+4−0
⇒r=√5
Now, the image of the centre in the given line is
x−13=y−2−4=−2(3×1−4×2+30)32+(−4)2⇒x=−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+(y−10)2=5