Question

The equation of a circle is x^2 + y^2 -4x + 2y -11 =0 . What are the center and the radius of the circle? Show your work.

Answer 1

Answer:

Center: (2,-1)

Radius: 4 units

Step-by-step explanation:

Equation of the circle in standard form is:

$x^{2}+y^{2}+2gx+2fy+c=0$

The radius of this circle is located at (-g, -f) and its radius is equal to:

$r=\sqrt{g^{2}+f^{2}-c}$

The given equation of circle is:

$x^{2}+y^{2}-4x+2y-11=0$

Re-writing this equation in a form similar to the standard equation:

$x^{2}+y^{2}+2(-2)x+2(1)y-11=0$

Comparing this equation with standard equation we can say:

g= -2

f = 1

c = -11

So, the center of the circle will be located at (-g, -f) = (2, -1)

And the radius will be = $\sqrt{g^{2}+f^{2}-c} =\sqrt{(-2)^{2}+(1)^{2}-(-11)} =\sqrt{16} =4$

Thus the radius of the given circle is 4 units.