Identify the center and radius of the circle with given equation

Question

4x²+4y²+40x-32y=5

Answer 1

4x²+4y²+40x-32y=5

We can put a skeleton this way:

4x²+40x+___ +4y²-32y+___=5+__+___

Factor out 4 for each trinomial and then do the process of completing the square:

4(x²+10x+___ )+4(y²-8y+___) =5+__+___

4(x²+10x+25 )+4(y²-8y+16) =5+4*25+4*16

Factor the ones in parentheses and simplify the right side:

4(x+5)² +4(y-4)² = 169

Divide 4 both sides of the equation:

(x+5)² +(y-4)² = 169/4

Now the equation of the circle is in standard form

(x-h)² +(y-k)² = r²

and we can identify the center (h,k)= (-5,4) and radius r = 13/2