Question

How do you find the domain and range of a circle?

Answer 1

Hint:We have to generalize the result in the form of the radius and the center of the circle. To do that, we first bring the equation of the circle into its general form. Then we apply the formula to it so that we get some acceptable values for the domain and range of the circle.

Formula Used:
The standard equation of a circle is:
\[{\left( {x - a} \right)^2} + {\left( {y - b} \right)^2} = {r^2}\]

Complete step by step answer:
Let there be a circle with given equation,
\[{\left( {x - a} \right)^2} + {\left( {y - b} \right)^2} = {r^2}\]
The domain of the circle is given by,
\[{D_f} = \left[ {a - r,a + r} \right]\]

And similarly, the range of the circle is given by,
\[{R_f} = \left[ {b - r,b + r} \right]\]

Note: In the given question, we were asked to find the domain and range of a circle. To do that, we first bring the equation of the circle into its general form. Then we applied some formulae to it so that we get some acceptable values for the domain and range of the circle. So, it is really important that we know the formulae and where, when and how to use them so that we can get the correct result.