Answer: The answer is (B) circle.
Step-by-step explanation: The given equation of the conic section is
[tex]x^2-4x+y^2-4y+4=12.[/tex]
We are to select the correct type of the conic section from the given options.
Let us try to find the standard form of the given conic section as follows:
[tex]x^2-4x+y^2-4y+4=12\\\\\Rightarrow (x^2-4x+4)+(y^2-4y+4)=12+4\\\\\Rightarrow (x-2)^2+(y-2)^2=16\\\\\Rightarrow (x-2)^2+(y-2)^2=4^2.[/tex]
Therefore, the given conic section is a circle with centre (2, 2) and radius 4 units.
The image of the circle is shown in the attached figure.
Thus, (b) Circle is the correct option.
