Consider the equation x^2 + (y-2)^2 = 1and the relation "(x, y)R(0, 2)", whereRis read as "has distance 1 of".

For example, "(0, 3)R(0, 2)", that is, "(0, 3) has distance 1 of (0, 2)". This relation can also be read as "the point (x, y) is on the circle of radius 1 with center (0, 2)". In other words: "(x, y) satisfies this equation, x^2 + (y-2)^2 = 1 if and only if, (x, y)R(0, 2)".

Does this equation determine a relation betweenxandy? Can the variablexcan be seen as a function ofy, likex=g(y)?Can the variableybe expressed as a function ofx, like y= h(x)? If these are possible, then what will be the domains for these two functions?What are the graphs of these two functions?

Are there points of the coordinate axes that relate to (0, 2) by means ofR?

Question: Where do I begin to solve this problem?