Question

Please help me asap!

Answer 1

ANSWER

The correct answer is D.

Step-by-step explanation

The given equation of the circle is

`{x}^(2) + {y}^(2) - 6x + 4y - 51 = 0`

We rewrite to obtain,


`{x}^(2) - 6x + {y}^(2) + 4y = 51`

We complete the the square to get,


`{x}^(2) - 6x + ( - 3)^(2)+ {y}^(2) + 4y + {(2)}^(2) = 51 +( - 3)^(2) + {(2)}^(2).`


`(x - 3)^(2) + {(y + 2)}^(2) = 51 +9+ 4`


`(x - 3)^(2) + {(y + 2)}^(2) =64`


`(x - 3)^(2) + {(y + 2)}^(2) = {8}^(2)`

Comparing to the equation of the circle in standard form


`(x - h)^(2) + {(y - k)}^(2) = {r}^(2)`

The centre of the circle is


`(h,k)=(3,-2)`

and radius

`r = 8`

The correct answer is D.