# Identify this conic section x^{2} - 4x + y^{2} - 4y + 4 = 12.

Line, circle, ellipse, parabola, hyperbola

**Solution:**

The equation of the conic section is

x^{2} - 4x + y^{2} - 4y + 4 = 12

Let us find the standard form

x^{2} - 4x + y^{2} - 4y + 4 = 12

By adding 4 on both sides and separating the terms

(x^{2} - 4x + 4) + (y^{2} - 4y + 4) = 12 + 4

(x - 2)^{2} + (y - 2)^{2} = 16

(x - 2)^{2} + (y - 2)^{2} = 4^{2}

Therefore, the conic section given is a circle with centre (2, 2) and radius 4.

## Identify this conic section x^{2} - 4x + y^{2} - 4y + 4 = 12.

**Summary:**

The conic section x^{2} - 4x + y^{2} - 4y + 4 = 12 is a circle with centre (2, 2) and radius 4.

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