Find the equation of the image of the circle `x^2+y^2+8x-16+64=0` in the line mirror `x=0.`

Explanation

The equation of the given circle is



`x^{2}+y^{2}+8 x-16 y+64=0 `


`Rightarrow(x^{2}+8 x+16)+ (y^{2}-16 y+64)=16`


`Rightarrow(x+4)^{2}+(y-8)^{2}=4^{2}`


`Rightarrow{x-(-4)}^{2}+(y-8)^{2}=4^{2}`


Clearly, its centre is at `(-4,8)` and radius `=4.`


The image of this circle in the line mirror has its centre `C_{1}(4,8) `and radius `4` . So, its equation is


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