Answer:
see explanation
Step-by-step explanation:
The equation of a circle in general form is
x² + y² + 2gx + 2fy + c = 0
with centre = (- g, - f) and radius = [tex]\sqrt{g^2+f^2-c}[/tex]
Given
2x² + 2y² + 6x - 8y + 12 = 0 ← divide through by 2
x² + y² + 3x - 4y + 6 = 0 ← in general form
Compare like terms
2g = 3 ⇒ g = [tex]\frac{3}{2}[/tex]
2f = - 4 ⇒ f = - 2 and c = 6, thus
centre = ( - [tex]\frac{3}{2}[/tex], 2 ) and
radius = [tex]\sqrt{(3/2)^2+(-2)^2-6}[/tex]
= [tex]\sqrt{\frac{9}{4}+4-6 }[/tex] = [tex]\sqrt{\frac{1}{4} }[/tex] = [tex]\frac{1}{2}[/tex]
