Question

Plzz help will mark brainliest

Answer 1

Answer:

Step-by-step explanation:

x^2 + 11y + y^2 -3x + 11 = 5x +23 - y

First put it into general form by setting the equation to zero  and moving all variables to one side.

x^2 + 11y + y^2 -3x + 11 = 5x +23 - y

       +y              -5x -11           -11

x^2 + y^2 - 8x + 12y = 12

Then solve by completing the square

x^2 - 8x         y^2 + 12y        = 12

(x -    )^2 + (y +   )^2 =

Half of 8 is 4

Then square 4 to get 16  

Therefore, we plug the 4 into the first parentheses

x^2 - 8x + 16 + y^2 + 12y      =12 +16

(x - 4)^2 + (y +  )^2 =

Half of 12 is 6

Squared, that would be 36

plug this into the second parentheses

x^2 - 8x + 16 + y^2 +12y + 36 = 12 + 16 + 36

(x - 4)^2 + (y + 6)^2 =

12 + 16 = 28 + 36 = 64

Therefore, the equation of the circle is: (x - 4)^2 + (y + 6)^2 = 64

Which is option D