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rewrite the equation of the circle (x − 2)2 + y2 = 3 in general form.

x² + y² - 4x + 1 = 0

Step-by-step explanation:

The equation of a circle in general form is

x² + y² + 2gx + 2fy + c = 0

Given

(x - 2)² + y² = 3 ← expand the squared factor

x² - 4x + 4 + y² = 3 ( subtract 3 from both sides )

x² + y² - 4x + 1 = 0 ← in general form

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guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: