Question

please help me asap!

Answer 1

ANSWER

The correct answer is D.

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.