Chapter A5.1, Problem 33E

To determine

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

Answer to Problem 33E

The center is [(7,-3)]

Explanation of Solution

Given:

  $2x^2+2y^2-28x+12y+114=0$

Calculation:

The given curve is:

  $2x^2+2y^2-28x+12y+114=0$

Converting it into standard form:

  ${(x-7)}^2+{(y+3)}^2=1$

Comparing with the standard form for a Circle:

  $X^2+Y^2=c^2$

We get,

  $c=1$

  $X=x-7$

  $Y=y+3$

Center is given by $(X,Y)=(0,0),$ or $(x-7,y+3)=(0,0)$

Therefore center is [(7,-3)]

Conclusion:

Therefore center is [(7,-3)]