Question

Find the center and radius of the circle with the given equation. Then select the correct graph of the X2 - 8x + y2 + 2y +1=0 The center is located at and the radius is

Answer 1

We will operate as follows:

$x^2-8x+y^2+2y+1=0\Rightarrow(x^2-8x)+(y^2+2y+1)=0$$\Rightarrow x(x-8)+(y^{}+1)^2=0\Rightarrow(x-4)^2+(y+1)^2=16$

Now, from this, we can see that the center of the circle is located at (4, -1).

The graph of the circle is the following: