Give the properties for the equation x 2 - 3 y 2 - 8x + 12y + 16 = 0 Center (4, -4) (4, 2) (4, -2)

Start by completing the square.

x^2-8x-3y^2+12y=-16
x^2-8x+16-3(y^2-4y+4)=-16+16-12=-12

Notice the addition of those constants allows us to factor these expressions and because we did it to both sides it’s completely legit.

(x-4)^2-3(y-2)^2=-12

However, it seems we get a negative radius, which is not allowed. I think you entered the problem incorrectly.