Answer:
B. (x-9)²+(y+4)²=69
Explanation:
The standard form of the equation of a circle is given as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Given the circle:
[tex]x^2-18x+y^2+8y+28=0[/tex]
Complete the square in each variable to obtain the standard form.
First, take the constant to the right-hand side of the equation.
[tex]x^2-18x+y^2+8y=-28[/tex]
Next, we divide the coefficient of x (same for y) by 2, square it and add it to both sides.
[tex]x^2-18x+(-9)^2+y^2+8y+(4^2)=-28+(-9)^2+(4^2)[/tex]
Write the left-hand side as a square while the right-hand side is simplified.
[tex](x-9)^2+(y+4)^2=69[/tex]
The correct choice is B.
