Chapter A5.1, Problem 32E

To determine

To find: the center, foci, vertices, asymptotes, and radius

Answer to Problem 32E

The center is [(-2,0)]

Explanation of Solution

Given:

  $x^2+4x+y^2=12$

Calculation:

The given curve is:

  $x^2+4x+y^2=12$

Converting it into standard form:

  ${(x+2)}^2+y^2=16$

Comparing with the standard form for a Circle

  $X^2+Y^2=c^2$

We get,

  $c=4$

  $X=x+2$

  $Y=y$

Center is given by $(X,Y)=(0,0),$ or $(x+2,y)=(0,0)$

Therefore center is [(-2,0)]

Conclusion:

Therefore center is [(-2,0)]