Find the Domain (3-h)^2+(-5-k)^2=2( square root of 7)^2

Problem

(3−h)2+(−5−k)2=2*(√(,7))2

Solution

1. Identify the equation as that of a circle by simplifying the constant on the right side.

2*(√(,7))2=2*(7)

2*(7)=14

2. Rewrite the equation in the standard form of a circle (x−(h_0))2+(y−(k_0))2=r2 where (h,k) are the variables representing the coordinates (x,y)

(h−3)2+(k+5)2=14

3. Determine the center and radius of the circle. The center is (3,−5) and the radius is r=√(,14)

r=√(,14)

4. Calculate the domain by finding the set of all possible values for the horizontal variable h The domain of a circle is [(h_0)−r,(h_0)+r]

Domain=[3−√(,14),3+√(,14)]

Final Answer

Domain=[3−√(,14),3+√(,14)]

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