Answer to Question #123081 in Algebra for Dani Wagas

Question #123081
Consider the equation x^2 + (y - 2)^2 = 1 and the relation "(x , y) R (0 , 2)", where R is 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 determined a relation between x and y ? Can the variable x be seen as a function of y, like x = g(y)? Can the variable y be expressed as a function of x, like y = h(x)?.
If these are possible, then what will be the domains for these two functions?
What are the graph of these two function?
Are there points of the coordinate axes that relate to (0 , 2) by means of R?
1
Expert's answer
2020-06-22T18:02:17-0400

Yes, This determines the relation between x and y as x and y are chosen in such a way that these form a circle of unit radius.

Hence we can say that x and y are related to each other i.e.

"(x-a)^2 + (y-b)^2 = 1" where (a,b) is the center of the circle.


If (a,b) is (0,2) then "x^2 + (y-2)^2 = 1"

then "x=g(y) = \\sqrt{1-(y-2)^2}" this is relation which shows the dependency of x on y


"y=h(x)= \\sqrt{1-x^2} + 2"



Domain for g(y) is [1,3] as y will take those values for which x is real. and that for h(x) is [0,1]



Point(0,2) is related by R as it will represent a circle of unit radius.




Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS