Question

can you help me with one other problem : x squared plus y squared plus 14x plus 18y plus 81=0.
find the center of the circle.

Answer 1

(-7,-9)

Answer 2

Radius 7

Answer 3

Because (x+7)^2-49=x^2+14x
And (y+9)^2-81=y^2+18y
So x^2+y^2+14x+18y+81=0
is the same as
(x+7)^2+(y+9)^2=7^2

Answer 4

(x+7)=0 when x=-7
(y+9)=0 when y=-9
center is (-7,-9)

Answer 5

\[x^2+14x+y^2+18y=-81\]
\[(x+7)^2+(y+9)^2=-81+7^2+9^2=-81+49+91=49\]
\[(x+7)^2+(y+9)^2=7^2\]
formula for circle with center ( h , k ) and radius r is
\[(x-h)^2+(y-k)^2=r^2\]
and you read off the answer. all the work is "completing the square"
\[x^2+14x\] complete by adding 49 to get
\[(x+7)^2\] since you add 49 to the left you must add 49 to the right. same for \[y^2+18y\] add 81 to get
\[(y+9)^2\]