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Find the image of the circle x^2+y^2-2x+...

Find the image of the circle `x^2+y^2-2x+4y-4=0` in the line `2x-3y+5=0`

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The image of the circle in the line will be circle having same radius, or given circle, centre is C(1,-2) and radius is `sqrt((-1)^(2)+(2)^(2)-(-4))=3`
Let image of C in the line be `C_(1)(h,k) `.
`:. (h-1)/(2)=(k+2)/(-3)=((-2(2(1))-3(2)+5))/((2)^(2)+(-3)^(2))= -2`
`:. h= -3 ` and `k=4`
Thus, centre of the image is `C_(1)(-3,4)`
Hence, equation of the image circle is `(x+3)^(2)+(y-4)^(2)=9`
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