Question

Complete the square for a circle. For #42.

Answer 1

we are given

`2x^2+2y^2-28x+20y+20=0`

we can see that

each terms are multiple of 2

so, we can factor out 2

`2(x^2+y^2-14x+10y+10)=0`

we can divide both sides by 2

`x^2+y^2-14x+10y+10=0`

we can rearrange it

`x^2+-14x+y^2+10y+10=0`

now, we can move 10 on right side

`x^2+-14x+y^2+10y=-10`

`x^2+-2*7*x+y^2+2*5*y=-10`

now, we can add both sides 7^2 and 5^2

`x^2+-2*7*x+7^2+y^2+2*5*y+5^2=-10+7^2+5^2`

`(x-7)^2+(y+5)^2=-10+7^2+5^2`

we can simplify it

`(x-7)^2+(y+5)^2=64`

we can also write as

`(x-7)^2+(y+5)^2=8^2`..............Answer