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