Question 167715
I'll do the first (which hopefully will help you do the second)



# 1





{{{x^2-8x+y^2+4y-205=0}}} Start with the given equation



{{{x^2-8x+y^2+4y=+205}}} Add {{{205}}} to both sides



{{{(x-4)^2-16+y^2+4y=205}}} Complete the square for the "x" terms. Note: Let me know if you need help completing the square.



{{{(x-4)^2-16+(y+2)^2-4=205}}} Complete the square for the "y" terms



{{{(x-4)^2+(y+2)^2-20=205}}} Combine like terms



{{{(x-4)^2+(y+2)^2=205+20}}} Add {{{20}}} to both sides



{{{(x-4)^2+(y+2)^2=225}}} Combine like terms





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Notice how the equation is now in the form {{{(x-h)^2+(y-k)^2=r^2}}}. This means that this conic section is a circle where (h,k) is the center and {{{r}}} is the radius.


So the circle has these properties:


Center: (4,-2)


Radius: {{{r=sqrt(225)=15}}}