Question

A certain circle can be represented by the following equation. x^2+y^2+18x+14y+105=0 What is the center of the circle? What is the radius of the circle?

Answer 1

Answer:

See below.

Step-by-step explanation:

Recall the equation for a circle:

$(x-h)^2+(y-k)^2=r^2$, where (h,k) is the center and r is the radius.

We need to turn the given equation into the above format. We do this by completing the square.

First, group them:

$(x^2+18x)+(y^2+14y)=-105$

For the first section, complete the square for $x^2+18x$:

$x^2+18x+81-81$

$(x+9)^2-81$

Do the same for the second:

$y^2+14y$

$y^2+14y+49-49$

$(y+7)^2-49$

All together:

$((x+9)^2-81)+((y+7)^2-49)=-105$

$(x+9)^2+(y+7)^2-130=-105$

$(x+9)^2+(y+7)^2=25$

The center is (-9,-7).

The radius is $\sqrt{25}=5$